Dubov was born in Leningrad but spent his young years in Yaroslavl. He studied in the Leningrad University under Mikhail Artamonov and later was a professor there. In 1972 he went to study the kurgans near Yaroslavl. It was Dubov's expedition that found in Timirevo the largest hoard of 9th-century Arabic dirhams in Eastern Europe.
Dubov was also the first to study runic graffiti on dirhams and published a monograph on the subject. In his dissertation he examined the phenomenon of "moving cities" in Gardariki. He was appointed Director of the Russian Ethnographic Museum in 1987.