Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in this Registration Statement on Form S-3 and related Prospectuses of KemPharm, Inc. of our report dated March 1, 2019 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, 2018.

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

/s/ RSM US LLP

Orlando, Florida

October 16, 2019