Yury Skobov won both the 10 km and relay at the first European Junior Cross-Country Skiing Championships in 1968 and he also repeated this feat at the next European Junior Championships in 1969. Skobov made his next international appearance at the 1972 Olympics, where he won gold as a member of the Soviet relay team and was fifth in the 15 km and 15th over 30 km.
At the 1974 World Championships Skobov won silver as a member of the Soviet relay team and made his last international appearance at the 1976 Olympics, where he was 16th at 15 km. Domestically Skobov won five Soviet titles – two in the 15 km (1972, 1973), one in the 30 km (1972) and two in the relay (1973, 1974). Skobov later worked as a director of the Metallurg Factory in his native Omutninsk.