Exhibit 99.1

TEXAS CAPITAL BANCSHARES, INC. ANNOUNCES PRICING OF PREFERRED STOCK OFFERING

DALLAS—March 21, 2013—Texas Capital Bancshares, Inc. (Texas Capital) (NASDAQ: TCBI), the parent company of Texas Capital Bank, today announced the pricing of a public offering of 6,000,000 shares, or $150 million in aggregate liquidation preference, of its 6.5% non-cumulative perpetual preferred stock, Series A, par value $.01. The preferred stock has a liquidation preference of $25 per share (the “Preferred Stock”). Texas Capital expects to use the net proceeds of this offering for general corporate purposes.

Morgan Stanley, BofA Merrill Lynch and J.P. Morgan are serving as joint book-running managers.

If declared, dividends will accrue and be payable on the liquidation preference amount, on a non-cumulative basis, at a rate of 6.5% per annum, quarterly, in arrears, on March 15, June 15, September 15 and December 15 of each year, beginning on June 15, 2013, from and including the date of original issuance. We may redeem the Preferred Stock as described in the prospectus supplement and accompanying base prospectus relating to the offering.

Texas Capital expects to close the transaction, subject to customary conditions, on or about March 28, 2013.

This press release does not constitute an offer to sell or a solicitation of an offer to buy, nor shall there be any sale of any of the securities in any jurisdiction in which such offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such jurisdiction. The securities being offered have not been approved or disapproved by any regulatory authority, nor has any such authority passed upon the accuracy or adequacy of the prospectus supplement.

This offering will be made only by means of a prospectus supplement and accompanying base prospectus. Texas Capital has filed a registration statement (including a base prospectus) and a preliminary prospectus supplement with the U.S. Securities and Exchange Commission (SEC) for the offering which this communication relates and will file a final prospectus supplement related to the offering. Copies of the final prospectus supplement and the accompanying base prospectus for the offering, when available, may be obtained from Morgan Stanley & Co. LLC, 180 Varick Street, New York, NY 10014, Attention: Prospectus Delivery Department or by emailing prospectus@morganstanley.com; from BofA Merrill Lynch, 222 Broadway, 11th Floor, New York, NY, 10038, Attn: Prospectus Department or by emailing dg.prospectus requests@baml.com; or from J.P. Morgan Securities, LLC, 383 Madison Avenue, New York, NY 10017, Attn: Investment Grade Syndicate Desk or by phone 212.834.4533.

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ABOUT TEXAS CAPITAL BANCSHARES, INC.

Texas Capital Bancshares, Inc.^® (NASDAQ: TCBI), a member of the Russell 2000^® Index and the S&P SmallCap 600^®, is the parent company of Texas Capital Bank, a commercial bank that delivers highly personalized financial services to businesses and private clients. Headquartered in Dallas, the bank has full-service locations in Austin, Dallas, Fort Worth, Houston and San Antonio.

This news release may be deemed to include forward-looking statements which are based on Texas Capital’s current estimates or expectations of future events or future results. Texas Capital is under no obligation, and expressly disclaims such obligation, to update, alter or revise its forward-looking statements, whether as a result of new information, future events, or otherwise. A number of factors, many of which are beyond Texas Capital’s control, could cause actual results to differ materially from future results expressed or implied by such forward-looking statements. These risks and uncertainties include, but are not limited to, the risk of adverse impacts from general economic conditions, competition, interest rate sensitivity and exposure to regulatory and legislative changes. These and other factors that could cause results to differ materially from those described in the forward-looking statements can be found in the prospectus supplement relating to the offering and the Annual Report on Form 10-K and other filings made by Texas Capital with the Securities and Exchange Commission (SEC).

This news release shall not constitute an offer to sell or a solicitation of an offer to buy any securities, nor shall there be any sale of any securities in any state or jurisdiction in which such an offer, solicitation or sale would be unlawful.

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