Thomas S. Harman

+1.202.373.6725

thomas.harman@morganlewis.com

VIA EDGAR

March 2, 2016

U.S. Securities and Exchange Commission

100 F Street, NE

Washington, DC 20549

RE:Nuveen AMT-Free Municipal Value Fund (File No. 333–183552 and 811-22253)

Dear Sir or Madam:

Pursuant to Rule 497(j) under the Securities Act of 1933, as amended (the “1933 Act”), I hereby certify on behalf of Nuveen AMT-Free Municipal Value Fund (the “Fund”) that the form of Prospectus and Statement of Additional Information that would have been filed pursuant to Rule 497(c) under the 1933 Act would not have differed from those included as part of Post-Effective Amendment No. 5 to the Fund’s Registration Statement on Form N-2, which was filed electronically with the SEC via EDGAR Accession No. 0001193125-16-481265 on February 26, 2016.

Please do not hesitate to contact me at (202) 373-6725 should you have any questions.

Very truly yours,

/s/ Thomas S. Harman

Thomas S. Harman