Exhibit l.1

March 7, 2019

Nuveen AMT-Free Quality Municipal Income Fund

333 West Wacker Drive

Chicago, Illinois 60606

Re:  Nuveen AMT-Free Quality Municipal Income Fund

Ladies and Gentlemen:

We have acted as special Massachusetts counsel to Nuveen AMT-Free Quality Municipal Income Fund, a Massachusetts business trust (the “Fund”), in connection with the Fund’s Post-Effective Amendment No. 3 to its Registration Statement on Form N-2 to be filed with the Securities and Exchange Commission (the “Commission”) on or about March 7, 2019 (the “Amendment”), with respect to 200,000 of its Series D MuniFund Preferred Shares of beneficial interest, $.01 par value per share, with a liquidation preference of $1,000 per share (the “Shares”).

In connection with the furnishing of this opinion, we have examined the following documents:

(a)    a certificate dated as of a recent date of the Secretary of the Commonwealth of Massachusetts as to the existence of the Fund;

(b)    copies of the Fund’s Declaration of Trust dated July 29, 2002, the amendment thereto dated as of November 18, 2009, and the name change amendments effective as of January 2, 2012 and September 12, 2016, each as on file in the office of the Secretary of the Commonwealth of Massachusetts (as so amended, the “Declaration”);

(c)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series 1 Variable Rate Demand Preferred Shares as filed at the office of the Secretary of the Commonwealth of Massachusetts on May 3, 2013;

(d)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series 2 Variable Rate Demand Preferred Shares as filed at the office of the Secretary of the Commonwealth of Massachusetts on May 3, 2013;

Morgan, Lewis & Bockius LLP           One Federal Street Boston, MA 02110-1726 United States      +1.617.341.7700  +1.617.341.7701

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March 7, 2019

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(e)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series 3 Variable Rate Demand Preferred Shares as filed at the office of the Secretary of the Commonwealth of Massachusetts on September 8, 2016;

(f)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series 4 Variable Rate Demand Preferred Shares as filed at the office of the Secretary of the Commonwealth of Massachusetts on September 8, 2016;

(g)     a copy of the Fund’s Amended and Restated Statement Establishing and Fixing the Rights and Preferences of Series 5 Variable Rate Demand Preferred Shares as filed at the office of the Secretary of the Commonwealth of Massachusetts on October 17, 2017;

(h)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series A MuniFund Preferred Shares, and the Supplement attached as Appendix A thereto as filed at the office of the Secretary of the Commonwealth of Massachusetts on February 7, 2018;

(i)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series B MuniFund Preferred Shares and the Supplement attached as Appendix A thereto, as filed at the office of the Secretary of the Commonwealth of Massachusetts on March 28, 2018, and as amended on October 1, 2018;

(j)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series C MuniFund Preferred Shares and the Supplement attached as Appendix A thereto as filed at the office of the Secretary of the Commonwealth of Massachusetts on March 28, 2018, and as amended on October 1, 2018;

(k)    a copy of the Fund’s Statement Establishing and Fixing the Rights and Preferences of Series D MuniFund Preferred Shares as filed at the office of the Secretary of the Commonwealth of Massachusetts on March 6, 2019 and the Supplement to the Statement Establishing and Fixing the Rights and Preferences of Series D MuniFund Preferred Shares initially Designating the Variable Rate Remarketed Mode for the Series D MuniFund Preferred Shares, as filed at the

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office of the Secretary of the Commonwealth of Massachusetts on March 6, 2019, and together with the Statements and, as applicable, the Supplements attached thereto, referred to in subparagraphs (c), (d), (e), (f), (g), (h), (i) and (j) above, the “Preferred Statements”;

(l)    a certificate executed by the Secretary of the Fund, certifying as to the Declaration, the Preferred Statements, and the By-Laws of the Fund (collectively, the “Governing Instruments”), certain resolutions adopted by the Fund’s Board of Trustees at meetings held on April 10-11, 2018, October 11, 2018, December 13, 2018 and January 24, 2019, the minutes of the meeting of the Fund’s Executive Committee held on March 5, 2019 (such resolutions and minutes, collectively, the “Resolutions”), and certain other matters; and

(m)     a printer’s proof of the Amendment received on March 6, 2019.

In such examination, we have assumed the genuineness of all signatures, the conformity to the originals of all of the documents reviewed by us as copies, the authenticity and completeness of all original documents reviewed by us in original or copy form and the legal competence of each individual executing any document. We have also assumed that the Amendment, when filed with the Commission, will be in substantially the form of the printer’s proof referenced in subparagraph (m) above.

This opinion is based entirely on our review of the documents listed above and such investigation of law as we have deemed necessary or appropriate. We have made no other review or investigation of any kind whatsoever, and we have assumed, without independent inquiry, the accuracy of the information set forth in such documents. We have further assumed that there are no other documents that are contrary to or inconsistent with the opinions expressed herein. As to our opinion below relating to the valid existence of the Fund, our opinion relies entirely upon and is limited by the certificate referenced in subparagraph (a) above.

This opinion is limited solely to the laws of the Commonwealth of Massachusetts as applied by courts located in such Commonwealth, except that we express no opinion as to any Massachusetts securities law. No opinion is given herein as to the choice of law or internal substantive rules of law which any tribunal may apply. In addition, to the extent that the Fund’s Governing Instruments refer to, incorporate or require compliance with the Investment

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Company Act of 1940, as amended, or any other law or regulation applicable to the Fund, except for the internal substantive laws of the Commonwealth of Massachusetts, as aforesaid, we have assumed compliance by the Fund with such Act and such other laws and regulations. Further, we express no opinion with respect to, and we assume no responsibility for, any offering documentation relating to the Fund, including the Amendment.

We understand that all of the foregoing assumptions and limitations are acceptable to you.

Based upon and subject to the foregoing, please be advised that it is our opinion that:

1. The Fund has been formed and is validly existing under the Fund’s Declaration and the laws of the Commonwealth of Massachusetts as a voluntary association with transferable shares of beneficial interest commonly referred to as a “Massachusetts business trust.”

2. The Shares, when issued and sold in accordance with the terms, conditions, requirements and procedures set forth in the Governing Instruments and the Resolutions, will be validly issued, fully paid and nonassessable, except that, as set forth in the Amendment, shareholders of the Fund may under certain circumstances be held personally liable for its obligations.

This opinion is given as of the date hereof and we assume no obligation to update this opinion to reflect any changes in law or any other facts or circumstances which may hereafter come to our attention. We hereby consent to the reference to our name in the Amendment and in the prospectus forming a part thereof under the heading “Legal Matters” and to the filing of this opinion as an exhibit to the Amendment. In rendering this opinion and giving this consent, we do not concede that we are in the category of persons whose consent is required under Section 7 of the 1933 Act.

Very truly yours,

/S/ MORGAN, LEWIS & BOCKIUS LLP

MORGAN, LEWIS & BOCKIUS LLP