SUBORDINATED DEBENTURE

Exhibit 10.3

SUBORDINATED DEBENTURE

SAVINGS ACCOUNT

OR DEPOSIT AND IT IS NOT INSURED BY THE FEDERAL

DEPOSIT INSURANCE CORPORATION OR ANY FEDERAL AGENCY.

FOR VALUE RECEIVED, the undersigned, INDEPENDENT BANK GROUP, INC., a bank holding company incorporated under the laws of the State of Texas, having its principal place of business at 2530 El Dorado Parkway, Suite 200, McKinney, Texas 75070 (the “Borrower”), hereby promises to pay to the order of TIB THE INDEPENDENT BANKERSBANK, a Texas state banking association and member of the Federal Reserve System having a place of business at 350 Phelps Drive, Irving, Texas 75038 (the “Lender”), or any holder hereof from time to time (the “Lender”), at such place as may be designated in writing by the Lender, the principal sum of FOUR MILLION FIVE HUNDRED THOUSAND AND NO/100 DOLLARS ($4,500,000.00) (or so much thereof that has been advanced and remains outstanding) with interest thereon as hereinafter provided. This Subordinated Debenture (this “Subordinated Debenture”) is issued pursuant to the terms of a Loan and Subordinated Debenture Purchase Agreement of even date herewith by and between the Borrower and the Lender (as may be amended, restated, supplemented or modified from time to time, the “Agreement”). All capitalized terms used but not defined herein shall have the respective meanings ascribed to them in the Agreement.

All accrued interest and unpaid principal due and payable under this Subordinated Debenture shall be paid in full on or before the Subordinated Debt Maturity Date.

The unpaid principal amount outstanding under this Subordinated Debenture from time to time shall bear interest before maturity in accordance with the Agreement, computed on the basis of a 360-day year and charged for actual days elapsed. Under certain circumstances as provided in the Agreement, overdue interest payments under this Subordinated Debenture shall bear interest from the due date thereof until paid at a daily rate equal to the Default Rate of Interest, computed on the basis of a 360-day year and charged for actual days elapsed, except as otherwise provided in the Loan Agreement.

All accrued but unpaid interest on the principal balance of the Subordinated Debt outstanding from time to time shall be payable on (a) the last Business Day of each calendar year beginning with March 31, 2009, and (b) the Subordinated Debt Maturity Date. The Borrower shall pay to the Lender the aggregate outstanding principal amount of all of the Subordinated Debt as follows: (i) twenty-four (24) consecutive quarterly principal installments of $187,500 [to be based on a six (6) year amortization] each due and payable on the last Business Day of each calendar quarter beginning with March 31, 2011; and (ii) one final installment in the amount of all unpaid principal of the Subordinated Debt due and payable on the Subordinated Debt Maturity Date. There shall be no penalties or other charges payable by the Borrower to the Lender hereunder other than those payments described in this Subordinated Debenture or in the

Loan Agreement. Except as otherwise provided in the Agreement, the Borrower may prepay all or, from time to time, part of the outstanding unpaid principal balance under this Subordinated Debenture at any time without a prepayment fee; provided, however, that Borrower may not prepay any portion of this Subordinated Debenture prior to the date that is two (2) years after the Closing Date of the Subordinated Debt.

This Subordinated Debenture is not secured by any assets of the Borrower.

So long as any portion of the unpaid principal of this Subordinated Debenture is deemed to be Tier 2 Capital of the Borrower in accordance with the rules and regulations of the FRB applicable to the capital status of the subordinated debt of bank holding companies, the rights of the Lender to the principal sum hereunder or any part hereof and to any accrued interest thereon shall remain subject and subordinate (in accordance with SR 92-37 issued by the FRB on October 15, 1992) to the claims of creditors of the Borrower with respect to the following (“Senior Claims”): (a) borrowed and purchased money; (b) similar obligations arising from offbalance-sheet guaranties and direct-credit substitutes; and (c) obligations associated with derivative products such as interest-rate and foreign exchange-rate contracts, commodity contracts, and similar arrangements (clauses (a), (b) and (c) expressly exclude Trust Preferred Indebtedness, as defined below, with respect to which the rights of the Lender are senior in all respects). Upon dissolution or liquidation of the Borrower, no payment of principal, interest or premium (including post-default interest) shall be due and payable under the terms of this Subordinated Debenture until all Senior Claims (which expressly exclude claims relating to the Trust Preferred Indebtedness) shall have been paid in full. If this Subordinated Debenture ceases to be deemed to be Tier 2 Capital of the Borrower in accordance with the rules and regulations of the FRB applicable to the capital status of the subordinated debt of bank holding companies, other than due to the limitations imposed by the second sentence of 12 C.F.R. 250.166(e)(1), which limits the capital treatment of subordinated debt during the five years immediately preceding the maturity date of the subordinated debt, the Borrower shall immediately notify the Lender, and immediately upon request of the Lender execute and deliver all such agreements (including without limitation pledge agreements and replacement notes) as the Lender may request in order to restructure the obligation evidenced hereby as a senior, secured obligation of the Borrower. If the Borrower fails to execute such agreements as required by the Lender within 30 days of the Lender’s request, such failure shall be deemed to be a Default under Section 5.1 of the Agreement.

As used herein, “Trust Preferred Indebtedness” shall mean indebtedness incurred in connection with, or relating to, any trust preferred securities caused to be issued by, or reflected in the consolidated financial statements of, the Borrower, including the subordinated indebtedness evidenced by the TP Junior Subordinated Debentures.

If a Default shall occur, the Lender shall have the rights set forth in Section 5.7 of the Loan Agreement.

If any attorney is engaged by the Lender to enforce or defend any provision of this Subordinated Debenture or any of the other Loan Documents, or as a consequence of any Event of Default, with or without the filing of any legal action or proceeding, then the Borrower shall pay to the Lender immediately upon demand all attorneys’ fees and expenses, together with interest thereon from the date of such demand until paid at the rate of interest applicable to the principal balance owing hereunder as if such unpaid attorneys’ fees and expenses had been added to the principal.

2

No previous waiver and no failure or delay by the Lender in acting with respect to the terms of this Subordinated Debenture or any of the other Documents shall constitute a waiver of any breach, default or failure of condition under this Subordinated Debenture, the Agreement or any of the other Loan Documents or the obligations secured thereby. A waiver of any term of this Subordinated Debenture or any of the other Loan Documents or of any of the obligations secured thereby must be made in writing and shall be limited to the express written terms of such waiver. In the event of any inconsistencies between the terms of this Subordinated Debenture and the terms of any other document related to the Loan evidenced by this Subordinated Debenture, the terms of this Subordinated Debenture shall prevail.

Except as otherwise provided in the Agreement, the Borrower expressly waives presentment, demand, notice of dishonor, notice of default or delinquency, notice of acceleration, notice of protest and nonpayment, notice of costs, expenses or losses and interest thereon, notice of late charges, and diligence in taking any action to collect any sums owing under this Subordinated Debenture. In addition, the Borrower expressly agrees that this Subordinated Debenture and any payment coming due hereunder may be extended from time to time without in any way affecting the liability of any such party hereunder.

Time is of the essence with respect to every provision hereof. This Subordinated Debenture shall be construed and enforced in accordance with the laws of the State of Texas, except to the extent that federal laws preempt the laws of the State of Texas, and all Persons in any manner obligated under this Subordinated Debenture consent to the jurisdiction of any federal or State court within the State of Texas having proper venue and also consent to service of process by any means authorized by Texas or Federal law. Any reference contained herein to attorneys’ fees and expenses shall be deemed to be to reasonable fees and expenses and to include all reasonable fees and expenses of in-house or staff attorneys and the reasonable fees and expenses of any other experts or consultants.

All agreements between the Borrower and the Lender (including, without limitation, this Subordinated Debenture and the Agreement, and any other documents securing all or any part of the indebtedness evidenced hereby) are expressly limited so that in no event whatsoever shall the amount paid or agreed to be paid to the Lender exceed the highest lawful rate of interest permissible under applicable law. If, from any circumstances whatsoever, fulfillment of any provision hereof, the Agreement or any other documents securing all or any part of the indebtedness evidenced hereby at the time performance of such provisions shall be due, shall involve exceeding the limit of validity prescribed by law which a court of competent jurisdiction may deem applicable hereto, then, ipso facto, the obligation to be fulfilled shall be reduced to the highest lawful rate of interest permissible under such applicable laws, and if, for any reason whatsoever, the Lender shall ever receive as interest an amount which would be deemed unlawful under such applicable law, such interest shall be automatically applied to the payment of the principal of this Subordinated Debenture (whether or not then due and payable) and not to the payment of interest or refunded to the Borrower if such principal has been paid in full.

3

The Lender may sell, assign, pledge or otherwise transfer or encumber any or all of its interest under this Subordinated Debenture at any time and from time to time. In the event of a transfer, all terms and conditions of this Subordinated Debenture shall be binding upon and inure to the benefit of the transferee after such transfer.

Upon receipt of notice from the Lender advising the Borrower of the loss, theft, destruction or mutilation of this Subordinated Debenture, the Borrower shall execute and deliver in lieu thereof a new debenture in principal amount equal to the unpaid principal amount of such lost, stolen, destroyed or mutilated debenture, dated the date to which interest has been paid on such lost, stolen, destroyed or mutilated Subordinated Debenture.

Unless otherwise provided in the Agreement, all payments on account of the indebtedness evidenced by this Subordinated Debenture shall be first applied to the payment of costs and expenses of the Lender which are due and payable, then to past-due interest on the unpaid principal balance and the remainder to principal.

Any notice which either party hereto may be required or may desire to give hereunder shall be governed by the notice provisions of the Agreement.

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4

THE BORROWER HEREBY KNOWINGLY, VOLUNTARILY AND INTENTIONALLY WAIVES ANY RIGHT THAT IT MAY HAVE TO A TRIAL BY JURY IN ANY LITIGATION ARISING IN ANY WAY IN CONNECTION WITH THIS SUBORDINATED DEBENTURE OR ANY OF THE OTHER LOAN DOCUMENTS, OR ANY OTHER STATEMENTS OR ACTIONS OF THE BORROWER OR THE LENDER, THE BORROWER ACKNOWLEDGES THAT IT HAS BEEN REPRESENTED IN THE SIGNING OF THIS SUBORDINATED DEBENTURE AND IN THE MAKING OF THIS WAIVER BY INDEPENDENT LEGAL COUNSEL SELECTED OF ITS OWN FREE WILL, AND THAT IT HAS DISCUSSED THIS WAIVER WITH SUCH LEGAL COUNSEL. BORROWER FURTHER ACKNOWLEDGES THAT (i) IT HAS READ AND UNDERSTANDS THE MEANING AND RAMIFICATIONS OF THIS WAIVER, (ii) THIS WAIVER HAS BEEN REVIEWED BY BORROWER AND BORROWER’S COUNSEL AND IS A MATERIAL INDUCEMENT FOR THE LENDER TO ENTER INTO THE LOAN DOCUMENTS, AND (iii) THIS WAIVER SHALL BE EFFECTIVE AS TO EACH OF THE LOAN DOCUMENTS AS IF FULLY INCORPORATED THEREIN.

IN WITNESS WHEREOF, the Borrower has caused this Subordinated Debenture to be duly executed as of the date first above written.