Belits-Geiman began swimming when he was eight. He was affiliated with the Moscow club Dynamo, and became a member of the Soviet swimming team in 1962. He competed at the
1964 Olympics in Tokyo, and finished in seventh place in the 4 × 200 m freestyle relay and eighth in the 400 meter freestyle. In 1966, he won the gold medal against three of the best American freestyle swimmers in a US vs USSR competition in Moscow. In 1966, he was ranked number three in the world in the 1,500-meter freestyle. That was 4.1 seconds faster than the former record set by Australian
Murray Rose in 1962. Due to a Soviet boycott, he was unable to defend his title at the
1967 Universiade in Tokyo. Americans Greg Charlton and
Mike Burton. He did, however, win silver medals in the 400 and 1500 meter freestyle at the 1967 Little Olympic swimming competitions held at the CDOM aquatic center in Mexico City. He won a silver medal at the
1968 Summer Olympics in
Mexico City in the 4×100 freestyle relay (3:34.2), swimming the lead leg, and a
bronze medal in the 4 × 200 m freestyle relay (8:01.6), swimming the second leg. In the 4 × 200 m relay, one of his teammates was
Vladimir Bure. He also swam two individual freestyle events, finishing seventh in the 200 m freestyle, and ninth in the 400 m race. He broke 67 Soviet national freestyle records. In 1974, he was named president of the Moscow Swim Federation and vice president of the Soviet Union Federation. ==Post-swimming career==