Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in Registration Statement (No. 333-196627) on Form S-3 pertaining to a shelf registration statement; and Registration Statement (No. 333-198483) on Form S-8 pertaining to the Independent Bank 401(k) Profit Sharing Plan, of our report dated February 27, 2015, relating to our audit of the consolidated financial statements, which appear in the Annual Report to Shareholders, which is incorporated in this Annual Report on Form 10-K of Independent Bank Group, Inc. for the year ended December 31, 2014.

/s/ McGladrey LLP