Rafig Babayev was born in Baku.

He studied at music school No. 160 (1943-1950), music school named after Asaf Zeynalli (R. Levina's class), and the Azerbaijan State Conservatory (1959).

In 1967, he was invited to the position of music director of the Song Theater. The ensemble was a laureate at the International Jazz Festival (Tallinn) (1967). In 1991, he organized the "Jangi" folklore-jazz ensemble and the Recording Studio. For many years, he was the artistic director of the variety-symphonic orchestra of the Azerbaijan State Television and Radio Company.

Honored Artist (1978), People's Artist (1993) Rafig Babayev died in a terrorist attack in the metro on March 19, 1994.