At the 1980 Summer Olympics, Vladimir Muravyov was sixth in the 100 metres final, but went out in the heats of the 200 metres, but he ran the opening leg in the Soviet 4×100 m relay team, which won the gold medal. At the 1982 European Championships, Muravyov was seventh in 200 m. At the first World Championships he reached the semifinal in 200 m and was a member of Soviet 4×100 m relay team, which won the bronze.