Grigori Kriss won four Olympic medals in three Olympiads. He captured a gold medal in Individual Epee at the 1964 Games. In 1968, he earned silvers in both the Individual Epee and Team Epee events. In 1972, Kriss won a bronze medal in Team Epee.

In World Championships competition, Kriss won the Individual Epee silver medal in 1967, and Individual gold medal in 1971. He won four World Team Epee medals: bronze in 1965, silver in 1966, gold in 1969, and silver in 1971.