Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in this Amendment No. 1 to the Registration Statement on Form S-3 (No. 333-234235) and related Prospectuses of KemPharm, Inc. of our report dated February 28, 2020 relating to the financial statements of KemPharm, Inc., appearing in the Annual Report on Form 10-K of KemPharm, Inc. for the year ended December 31, 2019.

We also consent to the reference to our firm under the heading “Experts” in such Prospectuses.

/s/ RSM US LLP

Orlando, Florida

March 31, 2020