TRANSMERIDIAN EXPLORATION INCORPORATED CONVERTIBLE PROMISSORY NOTE

Exhibit 10.3

THIS NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR ANY STATE SECURITIES LAW AND MAY NOT BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS REGISTERED UNDER THE SECURITIES ACT AND UNDER APPLICABLE STATE SECURITIES LAWS OR THE COMPANY SHALL HAVE RECEIVED AN OPINION OF COUNSEL THAT REGISTRATION OF SUCH SECURITIES UNDER THE SECURITIES ACT AND UNDER THE PROVISIONS OF APPLICABLE STATE SECURITIES LAWS IS NOT REQUIRED.

TRANSMERIDIAN EXPLORATION INCORPORATED

CONVERTIBLE PROMISSORY NOTE

FOR VALUE RECEIVED, the undersigned, Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”), hereby promises to pay to the order of [                            ] or any future holder of this convertible promissory note (the “Payee”), at the principal office of the Payee set forth herein, or at such other place as the holder may designate in writing to the Company, the principal sum of up to [                    ] Dollars (U.S. $[                    ]), or such other amount as may be outstanding hereunder, together with all accrued but unpaid interest, in such coin or currency of the United States of America as at the time shall be legal tender for the payment of public and private debts and in immediately available funds, as provided in this convertible promissory note (the “Note”).

1. Principal and Interest Payments.

(a) The Company shall repay in full the entire principal balance then outstanding under this Note on the first to occur (the “Maturity Date”) of: (i) the Payment Date; or (ii) the acceleration of the obligations as contemplated by this Note. The “Payment Date” shall be December 15, 2005.

(b) Interest on the outstanding principal balance of this Note shall accrue at a rate of ten percent (10%) per annum, compounded quarterly. Interest on the outstanding principal balance of the Note shall be computed on the basis of the actual number of days elapsed and a year of three hundred and sixty (360) days and shall be payable on the Maturity Date. Furthermore, upon the occurrence of an Event of Default, then to the extent permitted by law, the Company will pay interest to the Payee, payable on demand, on the outstanding principal balance of the Note from the date of the Event of Default until payment in full at the rate of twelve percent (12%) per annum.

(c) The Company may not prepay the outstanding principal amount of this Note prior to the Maturity Date without the written consent of the Payee; provided, however, that after the Conversion Date (as defined below), the Company may prepay the outstanding principal amount of this Note together with interest accrued thereon or, if only a portion of this Note shall have been converted, any new note issued with respect to the principal amount not converted.

(d) Whenever any payment to be made shall be due on a Saturday, Sunday or a public holiday under the laws of the State of Texas, such payment may be due on the next succeeding business day and such next succeeding day shall be included in the calculation of the amount of accrued interest payable on such date.

2. Conversion of Note.

(a) On the date of the consummation by the Company of an offering of the Company’s equity securities (which for purposes of this Section 2 includes any securities convertible into or exercisable for any of the Company’s capital stock, but does not include any Exempt Securities, as defined below), this Note and all accrued and unpaid interest thereon shall be convertible, in whole or in part and at the option of the Payee, into a number of shares of such equity securities equal to the quotient obtained by dividing (i) the product of (x) the principal amount of this Note being converted by the Payee (together with all accrued and unpaid interest thereon) and (y) 1.10, by (ii) the price per security at which such equity securities are sold to other investors in such offering. The Company shall notify the Payee of the proposed closing date of any such offering no less than 3 business days, but no more than 5 business days, prior to such date

(b) In the event that the Payee elects to convert all or a portion of the Note pursuant to Section 2(a), the Payee shall surrender the Note to the Company, along with a written notice to the Company, in the manner specified in Section 9 hereof, at least 1 day prior to the date on which conversion is sought to become effective (the “Conversion Date”) that such Payee elects to convert the Note or a specified portion thereof on the Conversion Date, and such notice shall specify the names (and addresses) in which certificates for Conversion Shares (as defined below) are to be issued.

(c) If the Note is surrendered for conversion pursuant to Section 2(b), then promptly after the Conversion Date, the Company shall deliver or cause to be delivered to the Payee certificates representing the number of fully paid and non-assessable shares of the applicable equity securities (the “Conversion Shares”), into which the Note may be converted. Such conversion shall be deemed to have been made immediately prior to the close of business on the Conversion Date, so that the rights of the Payee as a holder of the Note shall cease with respect to the Note at such time (including, without limitation, the right to receive the principal amounts of the Note other than in the form of Conversion Shares), interest shall cease to accrue hereon and the person or persons entitled to receive the Conversion Shares deliverable upon conversion of the Note shall be treated for all purposes as having become the record holders of such Conversion Shares at such time. If this Note shall have been converted in part, the Company shall, at the time of delivery of the certificate or certificates representing Conversion

2

Shares, deliver to the Payee a new Note evidencing the rights of the Payee with respect to the remaining principal amount (and all accrued and unpaid interest thereon), which new Note shall in all other respects be identical with this Note, or at the request of the Payee, appropriate notation may be made on this Note and the same returned to the Payee. If the Company intentionally and willfully fails to deliver to the Payee such certificate or certificates pursuant to this Section 2(c) (free of any restrictions on transfer or legends, if such shares have been registered) in accordance herewith, prior to the tenth (10^th) Business Day after the receipt by the Company of (i) a written notice of Payee’s election to convert this Note, and (ii) this Note (the “Date of Receipt”), the Company shall pay to such Payee, in cash, on a per diem basis, an amount equal to 2% of the value of the undelivered Conversion Shares or shares of Common Stock issuable upon conversion of the Conversion Shares if the Conversion Shares do not consist of Common Stock (based on the current market price of the Common Stock on the Date of Receipt) per month until such delivery takes place.

(d) The Company covenants that it will at all times reserve and keep available out of its authorized shares of capital stock, solely for purpose of issue or delivery upon conversion of the Note as herein provided, such number of Conversion Shares as shall then be issuable or deliverable upon the conversion of the Note and such number of shares of Common Stock as shall then be issuable upon conversion of the Conversion Shares, if applicable. The Company covenants that all Conversion Shares which shall be so issuable or deliverable (and all shares of Common Stock issuable upon conversion of the Conversion Shares, if applicable) shall, when issued or delivered, be duly and validly issued and fully paid and non-assessable.

(e) Notwithstanding anything contained in this Note to the contrary, the number of Conversion Shares (if the Conversion Shares consist of the Company’s common stock, par value $0.0006 per share (the “Common Stock”) and otherwise the number of shares of Common Stock issuable upon conversion of the Conversion Shares), together with the number of shares of Common Stock issuable upon exercise of the warrants issued pursuant to the Purchase Agreement (as defined below) (such warrants, the “Warrants”, and such shares of Common Stock issuable upon exercise thereof, the “Warrant Shares”), shall not exceed 19.99% of the number of shares of Common Stock outstanding on the Closing Date, subject to appropriate adjustment for stock splits, stock dividends, or other similar recapitalizations affecting the Common Stock (the “Maximum Common Stock Issuance”), unless the issuance of shares hereunder and thereunder in excess of the Maximum Common Stock Issuance shall first be approved by the Company’s stockholders in accordance with applicable law and the By-laws and Certificate of Incorporation of the Company. If at any point in time and from time to time (each a “Trigger Date”), the number of Conversion Shares or shares of Common Stock issuable upon conversion of the Conversion Shares, as applicable, together with the number of Warrant Shares, would exceed the Maximum Common Stock Issuance but for this Section 2(e), then the Company shall promptly call a shareholders meeting to request shareholder approval for the issuance of Common Stock hereunder and thereunder in excess of the Maximum Common Stock Issuance. Following any approval by the shareholders of such an additional issuance, the Note shall be convertible into the number of shares of Common Stock determined pursuant to this Note without regard to the limitations provided in this Section 2(e).

3

(f) The Company shall use commercially reasonable efforts to consummate an offering of its equity securities prior to the Maturity Date. If the Company does consummate such an offering and the Payee elects to convert this Note or any portion of this Note pursuant to Section 2(a), then Payee shall participate in such transaction on substantially identical terms to those on which the other investors in such transaction participate, including, without limitation, warrant coverage, if applicable. Without limiting the generality of the foregoing, the Payee shall benefit from the registration and other rights granted to the other investors in such an offering with respect to the Conversion Shares, or the shares of Common Stock issuable upon conversion of the Conversion Shares, as applicable.

(g) “Exempt Securities” means any shares of Common Stock issued by the Company after the date of issuance of this Note that are: (i) Warrant Shares; (ii) shares issued or issuable pursuant to anti-dilution provisions of the Series A Cumulative Convertible Preferred Stock of the Company (the “Preferred Stock”); (iii) shares issued or issuable upon the conversion of the Preferred Stock; (iv) shares issued or issuable upon the exercise of any warrants or options outstanding as of the date of the issuance of this Note; (v) shares of Common Stock or Common Stock Equivalents (as defined in the Warrants) issued in connection with a bona-fide strategic transaction, partnership, joint venture or acquisition, except for shares of Common Stock or Common Stock Equivalents issued in connection with a transaction involving the entity that, as of the date of the Purchase Agreement (as defined below), owns a 50% interest in the Company’s principal operating subsidiary in Kazakhstan or (vi) shares of Common Stock issued in connection with any stock-based compensation plans of the Company in existence as of the date of the issuance of this Note, or any issuance (at issuance or exercise prices at or above fair market value) of Common Stock, stock awards or options under, or the exercise of options granted pursuant to, any Board approved employee stock option or similar plan for the issuance of options or capital stock of the Company or (vii) shares of Common Stock issued in connection with a bona-fide underwritten public offering.

3. Representations and Warranties of the Company. The Company represents and warrants to the Payee as follows:

(a) The Company has been duly incorporated and is validly existing and in good standing under the laws of the state of Delaware, with full corporate power and authority to own, lease and operate its properties and to conduct its business as currently conducted.

(b) This Note has been duly authorized, validly executed and delivered on behalf of the Company and is a valid and binding obligation of the Company enforceable against the Company in accordance with its terms, subject to limitations on enforcement by general principles of equity and by bankruptcy or other laws affecting the enforcement of creditors’ rights generally, and the Company has full power and authority to execute and deliver this Note and to perform its obligations hereunder.

(c) The execution, delivery and performance of this Note will not (i) conflict with or result in a breach of or a default under any of the terms or provisions of, (A) the Company’s certificate of incorporation or by-laws, or (B) any material provision of any

4

indenture, mortgage, deed of trust or other material agreement or instrument to which the Company is a party or by which it or any of its material properties or assets is bound, (ii) result in a violation of any material provision of any law, statute, rule, regulation, or any existing applicable decree, judgment or order by any court, Federal or state regulatory body, administrative agency, or other governmental body having jurisdiction over the Company, or any of its material properties or assets or (iii) result in the creation or imposition of any material lien, charge or encumbrance upon any material property or assets of the Company or any of its subsidiaries pursuant to the terms of any agreement or instrument to which any of them is a party or by which any of them may be bound or to which any of their property or any of them is subject.

(d) No consent, approval or authorization of or designation, declaration or filing with any governmental authority on the part of the Company is required in connection with the valid execution and delivery of this Note.

4. Events of Default. The occurrence of any of the following events shall be an “Event of Default” under this Note:

(a) the Company shall fail to make the payment of any amount of any principal outstanding for a period of three (3) business days after the date such payment shall become due and payable hereunder; or

(b) the Company shall fail to make any payment of interest for a period of three (3) business days after the date such interest shall become due and payable hereunder; or

(c) any representation, warranty or certification made by the Company herein or in the Convertible Promissory Note and Warrant Purchase Agreement of even date herewith (the “Purchase Agreement”) shall prove to have been false or incorrect or breached in any material respect on the date as of which made; or

(d) the holder of any indebtedness of the Company or any of its subsidiaries shall accelerate any payment of any amount or amounts of principal or interest on any indebtedness (“Indebtedness”) (other than the Indebtedness hereunder) prior to its stated maturity or payment date on account of a default by the Company or any of its subsidiaries under the documents or agreements evidencing such Indebtedness, the aggregate principal amount of which Indebtedness of all such persons is in excess of $1,000,000, whether such Indebtedness now exists or shall hereinafter be created, and such accelerated payment entitles the holder thereof to immediate payment of such Indebtedness which is due and owing and such indebtedness has not been discharged in full or such acceleration has not been stayed, rescinded or annulled within five (5) business days of such acceleration; or

(e) A judgment or order for the payment of money shall be rendered against the Company or any of its subsidiaries in excess of $1,000,000 in the aggregate (net of any applicable insurance coverage) for all such judgments or orders against all such persons (treating any deductibles, self insurance or retention as not so covered) that shall not be

5

discharged, and all such judgments and orders remain outstanding, and there shall be any period of sixty (60) consecutive days following entry of the judgment or order in excess of $1,000,000 or the judgment or order which causes the aggregate amount described above to exceed $1,000,000 during which a stay of enforcement of such judgment or order, by reason of a pending appeal or otherwise, shall not be in effect; or

(f) the Company shall (i) apply for or consent to the appointment of, or the taking of possession by, a receiver, custodian, trustee or liquidator of itself or of all or a substantial part of its property or assets, (ii) make a general assignment for the benefit of its creditors, (iii) commence a voluntary case under the United States Bankruptcy Code (the “Bankruptcy Code”) or under the comparable laws of any jurisdiction (foreign or domestic), (iv) file a petition seeking to take advantage of any bankruptcy, insolvency, moratorium, reorganization or other similar law affecting the enforcement of creditors’ rights generally, (v) acquiesce in writing to any petition filed against it in an involuntary case under the Bankruptcy Code or under the comparable laws of any jurisdiction (foreign or domestic), or (vi) take any action under the laws of any jurisdiction (foreign or domestic) analogous to any of the foregoing; or

(g) a proceeding or case shall be commenced in respect of the Company or any of its subsidiaries without its application or consent, in any court of competent jurisdiction, seeking (i) the liquidation, reorganization, moratorium, dissolution, winding up, or composition or readjustment of its debts, (ii) the appointment of a trustee, receiver, custodian, liquidator or the like of it or of all or any substantial part of its assets or (iii) similar relief in respect of it under any law providing for the relief of debtors, and such proceeding or case described in clause (i), (ii) or (iii) shall continue undismissed, or unstayed and in effect, for a period of thirty (30) consecutive days or any order for relief shall be entered in an involuntary case under the Bankruptcy Code or under the comparable laws of any jurisdiction (foreign or domestic) against the Company or any of its subsidiaries or action under the laws of any jurisdiction (foreign or domestic) analogous to any of the foregoing shall be taken with respect to the Company or any of its subsidiaries and shall continue undismissed, or unstayed and in effect for a period of thirty (30) consecutive days; or

(h) the suspension from listing or the failure of the Company’s common stock to be listed on any of the OTC Bulletin Board, American Stock Exchange, Nasdaq National Market or Nasdaq SmallCap Market for a period of five (5) consecutive trading days.

5. Remedies Upon An Event of Default. If an Event of Default shall have occurred and shall be continuing, the Payee of this Note may at any time at its option, (a) declare the entire unpaid principal balance of this Note, together with all interest accrued hereon, due and payable, and thereupon, the same shall be accelerated and so due and payable; provided, however, that upon the occurrence of an Event of Default described in (i) Sections 4(f) and (g), without presentment, demand, protest, or notice, all of which are hereby expressly unconditionally and irrevocably waived by the Company, the outstanding principal balance and accrued interest hereunder shall be automatically due and payable, and (ii) Sections 4(a) through (e) and Section 4(h), the Payee may exercise or otherwise enforce any one or more of the Payee’s

6

rights, powers, privileges, remedies and interests under this Note or applicable law. No course of delay on the part of the Payee shall operate as a waiver thereof or otherwise prejudice the right of the Payee. No remedy conferred hereby shall be exclusive of any other remedy referred to herein or now or hereafter available at law, in equity, by statute or otherwise.

6. Replacement. Upon receipt of a duly executed, notarized and unsecured written statement from the Payee with respect to the loss, theft or destruction of this Note (or any replacement hereof) and upon receipt of a written agreement of indemnification reasonably acceptable to the Company signed by the Payee (or holder at the time thereof) or, in the case of a mutilation of this Note, upon surrender and cancellation of such Note, the Company shall issue a new Note, of like tenor and amount, in lieu of such lost, stolen, destroyed or mutilated Note.

7. Parties in Interest, Transferability. This Note shall be binding upon the Company and its successors and permitted assigns and the terms hereof shall inure to the benefit of the Payee and its successors and assigns. This Note may be transferred or sold, subject to the provisions of Section 15 of this Note, or pledged, hypothecated or otherwise granted as security by the Payee.

8. Amendments. This Note may not be modified or amended in any manner except in writing executed by the Company and the Payee.

9. Notices. Any notice, demand, request, waiver or other communication required or permitted to be given hereunder shall be in writing and shall be effective (a) upon hand delivery by telecopy or facsimile at the address or number designated below (if delivered on a business day during normal business hours where such notice is to be received), or the first business day following such delivery (if delivered other than on a business day during normal business hours where such notice is to be received) or (b) on the second business day following the date of mailing by express courier service, fully prepaid, addressed to such address, or upon actual receipt of such mailing, whichever shall first occur. The Company will give written notice to the Payee at least twenty (20) days prior to the date on which dissolution, liquidation or winding-up will take place and in no event shall such notice be provided to the Payee prior to such information being made known to the public. Notices to the Payee and the Company shall be made to the addresses set forth in the Purchase Agreement.

10. Governing Law. This Note shall be governed by and construed in accordance with the internal laws of the State of New York, without giving effect to the choice of law provisions. This Note shall not be interpreted or construed with any presumption against the party causing this Note to be drafted.

11. Headings. Article and section headings in this Note are included herein for purposes of convenience of reference only and shall not constitute a part of this Note for any other purpose.

12. Remedies, Characterizations, Other Obligations, Breaches and Injunctive Relief. The remedies provided in this Note shall be cumulative and in addition to all other remedies available under this Note, at law or in equity (including, without limitation, a decree of

7

specific performance and/or other injunctive relief), no remedy contained herein shall be deemed a waiver of compliance with the provisions giving rise to such remedy and nothing herein shall limit a Payee’s right to pursue actual damages for any failure by the Company to comply with the terms of this Note. Amounts set forth or provided for herein with respect to payments and the like (and the computation thereof) shall be the amounts to be received by the Payee and shall not, except as expressly provided herein, be subject to any other obligation of the Company (or the performance thereof). The Company acknowledges that a breach by it of its obligations hereunder may cause irreparable and material harm to the Payee and that the remedy at law for any such breach may be inadequate. Therefore the Company agrees that, in the event of any such breach or threatened breach, the Payee shall be entitled, in addition to all other available rights and remedies, at law or in equity, to seek such equitable relief, including but not limited to an injunction restraining any such breach or threatened breach, without the necessity of showing economic loss and without any bond or other security being required.

13. Failure or Indulgence Not Waiver. No failure or delay on the part of the Payee in the exercise of any power, right or privilege hereunder shall operate as a waiver thereof, nor shall any single or partial exercise of any such power, right or privilege preclude other or further exercise thereof or of any other right, power or privilege.

14. Enforcement Expenses. The Company agrees to pay all costs and expenses of enforcement of this Note, including, without limitation, reasonable attorneys’ fees and expenses, to the extent the Payee prevails in such enforcement action.

15. Compliance with Securities Laws. The Payee of this Note acknowledges that this Note is being acquired solely for the Payee’s own account and not as a nominee for any other party, and for investment, and that the Payee shall not offer, sell or otherwise dispose of this Note other than in compliance with the laws of the United States of America and as guided by the rules of the Securities and Exchange Commission. This Note and any Note issued in substitution or replacement therefore shall be stamped or imprinted with a legend in substantially the following form:

“THIS NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR ANY STATE SECURITIES LAW AND MAY NOT BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS REGISTERED UNDER THE SECURITIES ACT AND UNDER APPLICABLE STATE SECURITIES LAWS OR THE COMPANY SHALL HAVE RECEIVED AN OPINION OF COUNSEL THAT REGISTRATION OF SUCH SECURITIES UNDER THE SECURITIES ACT AND UNDER THE PROVISIONS OF APPLICABLE STATE SECURITIES LAWS IS NOT REQUIRED.”

16. Severability. The provisions of this Note are severable, and if any provision shall be held invalid or unenforceable in whole or in part in any jurisdiction, then such invalidity or unenforceability shall not in any manner affect such provision in any other jurisdiction or any other provision of this Note in any jurisdiction.

8

17. Consent to Jurisdiction. Each of the Company and the Payee (i) hereby irrevocably submits to the jurisdiction of the United States District Court sitting in the Southern District of New York and the courts of the State of New York located in New York county for the purposes of any suit, action or proceeding arising out of or relating to this Note and (ii) hereby waives, and agrees not to assert in any such suit, action or proceeding, any claim that it is not personally subject to the jurisdiction of such court, that the suit, action or proceeding is brought in an inconvenient forum or that the venue of the suit, action or proceeding is improper. Each of the Company and the Payee consents to process being served in any such suit, action or proceeding by mailing a copy thereof to such party at the address set forth in Section 9 hereof and agrees that such service shall constitute good and sufficient service of process and notice thereof. Nothing in this Section 17 shall affect or limit any right to serve process in any other manner permitted by law.

18. Company Waivers. Except as otherwise specifically provided herein, the Company and all others that may become liable for all or any part of the obligations evidenced by this Note, hereby waive presentment, demand, notice of nonpayment, protest and all other demands and notices in connection with the delivery, acceptance, performance and enforcement of this Note, and do hereby consent to any number of renewals of extensions of the time or payment hereof and agree that any such renewals or extensions may be made without notice to any such persons and without affecting their liability herein and do further consent to the release of any person liable hereon, all without affecting the liability of the other persons, firms or Company liable for the payment of this Note, AND DO HEREBY WAIVE TRIAL BY JURY.

THE COMPANY ACKNOWLEDGES THAT THE TRANSACTION OF WHICH THIS NOTE IS A PART IS A COMMERCIAL TRANSACTION, AND TO THE EXTENT ALLOWED BY APPLICABLE LAW, HEREBY WAIVES ITS RIGHT TO NOTICE AND HEARING WITH RESPECT TO ANY PREJUDGMENT REMEDY WHICH THE PAYEE OR ITS SUCCESSORS OR ASSIGNS MAY DESIRE TO USE.

19. Payment Set Aside. To the extent that the Company makes a payment or payments to any Payee pursuant to this Note or a Payee enforces or exercises its rights hereunder, and such payment or payments or the proceeds of such enforcement or exercise or any part thereof are subsequently invalidated, declared to be fraudulent or preferential, set aside, recovered from, disgorged by or are required to be refunded, repaid or otherwise restored to the Company, a trustee, receiver or any other person under any law (including, without limitation, any bankruptcy law, state or federal law, common law or equitable cause of action), then to the extent of any such restoration the obligation or part thereof originally intended to be satisfied shall, to the extent permissible under applicable law, be revived and continued in full force and effect as if such payment had not been made or such enforcement or setoff had not occurred.

[REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

9

IN WITNESS WHEREOF, the Company has executed and delivered this Convertible Promissory Note as of the date first written above.

10