Nuveen High Income 2020 Target Term Fund (JHY) CORRESP Correspondence with SEC

Nuveen Investments

333 West Wacker, Suite 3300

Chicago, IL 60606

June 30, 2015

BY EDGAR

Securities and Exchange Commission

100 F Street, N.E.

Washington, DC 20549

Ladies and Gentlemen:

Nuveen High Income 2020 Target Term Fund

811-23051

333-203768

On behalf of the Nuveen High income 2020 Target Term Fund (the “Fund”), we hereby make the following representations:

(i) the Fund is responsible for the adequacy and accuracy of the disclosure in its filings with the Securities and Exchange Commission (the “Commission”);

(ii) should the Commission or the staff, acting pursuant to delegated authority, declare the filing effective, it does not foreclose the Commission from taking any action with respect to the filing;

(iii) the action of the Commission or the staff, acting pursuant to delegated authority, in declaring the filing effective, does not relieve the Fund from full responsibility for the adequacy and accuracy of the disclosure in the filings; and

(iv) the Fund may not assert this action as a defense in any proceeding initiated by the Commission or any person under the Federal securities laws of the United States.

NUVEEN HIGH INCOME 2020 TARGET TERM FUND

By: /s/ Gifford R. Zimmerman

Name: Gifford R. Zimmerman

Title: Chief Administrative Officer