Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our report dated April 10, 2014 (except for Note 15, as to which the date is February 9, 2015), with respect to the consolidated financial statements and financial statement schedule included in this Current Report on Form 8-K of Luna Innovations Incorporated. We hereby consent to the incorporation by reference of said report in the Registration Statements of Luna Innovations Incorporated on Form S-3 (File No. 333-191809) and on Form S-8 (File No. 333-138745).

/s/ Grant Thornton LLP

McLean, Virginia

February 9, 2015