Nuveen High Income 2020 Target Term Fund (JHY) POS EX Additional exhibits for listing

Exhibit l.3

K&L Gates LLP

70 W. Madison St.

Suite 3100

Chicago, IL 60602

July 29, 2015

Nuveen High Income 2020 Target Term Fund

333 West Wacker Drive

Chicago, Illinois 60606

Nuveen High Income 2020 Target Term Fund

As counsel for Nuveen High Income 2020 Target Term Fund (the “Registrant”), we consent to the incorporation by reference of our opinion, filed with Pre-effective Amendment No. 2 to the Registrant’s Registration Statement on Form N-2 (File Nos. 333-203768 and 811-23051) on June 22, 2015.

In giving this consent we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933.

Very truly yours,

/s/ K&L Gates LLP                                             

K&L Gates LLP