EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our reports dated March 3, 2014 with respect to the consolidated financial statements and schedule and internal control over financial reporting included in the Annual Report of Invesco Mortgage Capital Inc. on Form 10-K for the year ended December 31, 2013. We hereby consent to the incorporation by reference of said reports in the Registration Statements of Invesco Mortgage Capital Inc. on Forms S-3ASR (File No. 333-187647, effective April 1, 2013 and File No. 333-187646, effective April 1, 2013) and Form S-8 (File No. 333-163249, effective November 20, 2009).

/s/ Grant Thornton LLP

Philadelphia, Pennsylvania

March 3, 2014