Hacham Avraham Cohen was born to Rivka, daughter of Hanina, and Hacham Yaakov Cohen, in the city of Gafsa, Tunisia, and served as rabbi of the seaport city, Sfax. Hacham Avraham Cohen immigrated to the Land of Israel and settled in Jerusalem, where he served as rabbi of the Talpiot neighborhood.
Hacham Avraham Cohen was a very humble indovodual, who lived in a one-room apartment and devoted himself entirely to his community and to Torah study. He and his wife had three children, two sons and a daughter.
Hacham Avraham Cohen passed away on 24 Nissan, 5754 (1994). He wrote the following books: Melel LeAvraham and VaYosef Avraham, as well as a booklet, entitled Netsor Libcha.