Texas Capital Bancshares (TCBI) 10-K 2009 FY Annual report

EXHIBIT 32.1

CERTIFICATION

The undersigned hereby certifies, for the purposes of section 1350 of chapter 63 of title 18 of the United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, in his capacity as an officer of Texas Capital Bancshares, Inc. (“Texas Capital”), that, to his knowledge, the Annual Report of Texas Capital on Form 10-K for the period ended December 31, 2009, fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934 and that the information contained in such report fairly presents, in all material respects, the financial condition and results of operation of Texas Capital. This written statement is being furnished to the Securities and Exchange Commission as an exhibit to such Form 10-K. A signed original of this statement has been provided to Texas Capital and will be retained by Texas Capital and furnished to the Securities and Exchange Commission or its staff upon request.

/S/ George F. Jones, Jr.George F. Jones, Jr.

Chief Executive Officer

Date: February 18, 2010