20% Junior Redeemable Convertible Preferred StockAdditional Return Agreement

Exhibit 10.3

CONFIDENTIAL

June 26, 2007

Transmeridian Exploration Incorporated

397 N. Sam Houston Pkwy. E., Suite 300

Houston, Texas 77060

Attention: Earl W. McNiel, Chief Financial Officer

20% Junior Redeemable Convertible Preferred Stock Additional Return Agreement

Ladies and Gentlemen:

Reference is made to the Regulation D Purchase Agreement, dated the date hereof (the “Purchase Agreement”), by and among the various investors set forth on the signature pages thereto (collectively, the “Investors”) and Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”). Terms used but not defined in this Additional Return Agreement shall have the meanings assigned thereto in the Purchase Agreement.

As consideration for our respective agreements under the Purchase Agreement with respect to the Regulation D Placement, the Company hereby agrees to pay to each Investor a preferred return (collectively, and as the same may be adjusted as provided for below, the “Returns”) equal to 25% of the aggregate liquidation preference of the Securities to be purchased by such Investor pursuant to the Purchase Agreement, as set forth on Annex A to the Purchase Agreement entitled “Registration Information,” which preferred return is subject to adjustment as described below.

The Returns are fully vested upon consummation of the Regulation D Placement; provided, however, all Returns are due and payable at the earlier of: (i) the occurrence of a Change of Control (as defined in the Certificate of Designations) and (ii) June 18, 2008.

If the Returns are not paid by December 31, 2007, from and after such date the principal amount of the Company’s obligation to pay the Returns shall thereafter be increased, without the need for further act or evidence, at the rate of 10% per annum.

You shall make payment of the Returns when due without the need for any demand or other action by any of us, in each case by wire transfer to the respective accounts that each Investor shall have previously designated to you; provided, however, if the Returns become due other than upon the occurrence of a Change of Control, you may elect to satisfy your payment obligations with respect thereto by delivery of duly authorized, fully paid and non-assessable shares of your Common Stock, valued for such purpose as prescribed by Section (3A)(b) of the Certificate of Designations.

No Returns, once vested, are assignable without the prior written consent of the Company, which shall not unreasonably be withheld; provided, however, notwithstanding the foregoing, an Investor may assign its vested Returns, or any part thereof, to an affiliate and in such case the assignor must provide written notice thereof to the Company promptly upon completion of such assignment. Notwithstanding any provision of this Additional Return Agreement or the Purchase Agreement to the contrary, an Investor may elect in writing to waive all or any portion of its Returns, whether vested or unvested.

You agree that, once paid, the Returns or any part thereof payable hereunder will not be refundable under any circumstances. All Returns payable hereunder will be paid in immediately available funds and shall not be subject to reduction by way of setoff or counterclaim.

You agree that (i) you will not disclose this Additional Return Agreement or the contents hereof other than as permitted by the Purchase Agreement and (ii) your obligations under this Additional Return Agreement shall survive the expiration or termination of the Purchase Agreement and the purchase of the Securities.

It is understood that this Additional Return Agreement shall not constitute or give rise to any obligation on our part to purchase any Securities; such an obligation will arise only under the Purchase Agreement if accepted in accordance with its terms and executed and delivered. This Additional Return Agreement may not be amended or any provision hereof waived or modified except by an instrument in writing signed by each of the parties hereto. THIS ADDITIONAL RETURN AGREEMENT SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE

STATE OF NEW YORK. This Additional Return Agreement may be executed in any number of counterparts, each of which shall be an original and all of which, when taken together, shall constitute one agreement. Delivery of an executed counterpart of a signature page of this Additional Return Agreement by facsimile transmission shall be effective as delivery of a manually executed counterpart of this Additional Return Agreement. Section headings used herein are for convenience of reference only, are not part of this Additional Return Agreement and are not to affect the construction of, or to be taken into consideration in interpreting, this Additional Return Agreement.

Remainder of this page intentionally left blank

If the foregoing correctly sets forth our understanding, please indicate your acceptance of the terms hereof by returning to each of us an executed counterpart hereof, whereupon this Additional Return Agreement shall become a binding agreement between us.

Very truly yours,

Additional Return Agreement Signature Page

Additional Return Agreement Signature Page

Additional Return Agreement Signature Page

Additional Return Agreement Signature Page

Additional Return Agreement Signature Page