Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We have issued our report dated June 25, 2014, with respect to the financial statements and supplemental schedule of the SWS Group 401(k) Profit Sharing Plan on Form 11-K for the year ended December 31, 2013. We hereby consent to the incorporation by reference of said report in the Registration Statement of SWS Group, Inc. on Form S-8 (File No. 000-19483 effective October 11, 1991).

\s\ Grant Thornton LLP

Dallas, Texas

June 25, 2014