EXHIBIT (b)

Certification of CEO and CFO Pursuant to

18 U.S.C. Section 1350,

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Report on Form N-CSR of Advent Convertible and Income Fund (the “Company”) for the semi-annual period ended April 30, 2020 (the “Report”), Tracy V. Maitland, as President and Chief Executive Officer of the Company, and Robert White, as Treasurer and Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

(1) the Report fully complies with the requirements of Section 13(a) or 15(d) 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 operations of the Company.

Dated: July 2, 2020           

/s/ Tracy V. Maitland         

Name:  Tracy V. Maitland

Title:   Chief Executive Officer

/s/ Robert White               

Name:  Robert White

Title:   Chief Financial Officer