CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY

ACT OF 2002

I, Lisa M. Jones, certify that, to the best of my knowledge:

1. The Form N-CSR (the Report) of Pioneer High Income Fund, Inc., fully complies for the period covered by the Report with the requirements of Section 13(a) or 15 (d), as applicable, of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of the operations of the Fund.

Date: December 6, 2022

/s/ Lisa M. Jones

Lisa M. Jones

President and Chief Executive Officer

This certification is being furnished pursuant to Rule 30a-2(b) under the Investment Company Act of 1940, as amended, and 18 U.S.C. section 1350 and is not being filed as part of the Report with the Securities and Exchange Commission.

A signed original of this written statement required by section 906 has been provided to the Fund and will be retained by the Fund and furnished to the Securities Exchange Commission or its staff upon request.

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY

ACT OF 2002

I, Anthony J. Koenig, Jr., certify that, to the best of my knowledge:

1. The Form N-CSR (the Report) of Pioneer High Income Fund, Inc., fully complies for the period covered by the Report with the requirements of Section 13(a) or 15 (d), as applicable, of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of the operations of the Fund.

Date: December 6, 2022

/s/ Anthony J. Koenig, Jr.

Anthony J. Koenig, Jr.

Managing Director, Chief Operations Officer & Treasurer of the Funds

This certification is being furnished pursuant to Rule 30a-2(b) under the Investment Company Act of 1940, as amended, and 18 U.S.C. section 1350 and is not being filed as part of the Report with the Securities and Exchange Commission.

A signed original of this written statement required by section 906 has been provided to the Fund and will be retained by the Fund and furnished to the Securities Exchange Commission or its staff upon request.