Albert Filozov was born in the city of Sverdlovsk, RSFSR, USSR. Honored Artist of the RSFSR (29.03.1983). People's Artist of Russia (29.08.1994). He trained as a turner and worked at the "Sharopodshipnik" factory. In 1955, together with Yuriy Grebenshchikov, he was accepted by an visiting commission into the Moscow Art Theatre School-Studio (Viktor Stanitsyn's course). After finishing his studies in 1959, he worked for the 1959-1960 season at the Moscow Stanislavsky Drama Theatre under M.M. Yanshin, being introduced into E.P. Leonov's roles. In 1960-1961 he worked at the Yermolova Theatre. In 1961 he was drafted into the army and served two years in a sapper battalion.

In 1963 he returned to the Moscow Stanislavsky Drama Theatre (until 1984, formally listed until 1990). He worked with M.O. Knebel and A.A. Popov and played in Anatoly Vasilyev's productions. From 1982 he rehearsed with Anatoly Vasilyev at the Taganka Theatre Viktor Slavkin's play "Cerso", whose premiere took place in July 1985. From 1989 he played in productions of the "School of Contemporary Play" theatre. In 1991-1995 he was a master (together with Armen Dzhigarkhanyan) of an acting course at VGIK. He taught at RATI and was a professor of the department of drama directing (I.L. Raikhelgauz's workshop).