Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our reports dated March 10, 2014, with respect to the consolidated financial statements and internal control over financial reporting included in the Annual Report of New York Mortgage Trust, 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 New York Mortgage Trust, Inc. on Forms S-3 (File No. 333-186017 effective January 28, 2013, File No. 333-186016 effective January 14, 2013, File No. 333-179314 effective April 11, 2012, and File No. 333-150088 effective April 18, 2008) and on Forms S-8 (File No. 333-167609 effective June 17, 2010 and File No. 333-137987 effective October 13, 2006).

/s/ Grant Thornton LLP

New York, New York

March 10, 2014