Texas Capital Bancshares (TCBI) 10-Q 2013 Q3 Quarterly report

EXHIBIT 32.1

CERTIFICATION

In connection with the Quarterly Report of Texas Capital Bancshares, Inc. (the “Company”) on Form 10-Q for the period ending September 30, 2013 (the “Report”), as filed with the Securities and Exchange Commission on the date hereof, I, George F. Jones, Jr., Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of my knowledge:

1. The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report, fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ George F. Jones, Jr.

George F. Jones, Jr.

Chief Executive Officer

Date: November 12, 2013