Grishin trained for the largest part of his speedskating career at CSKA Moscow.

Along with his compatriot Lidiya Skoblikova, he was the most successful athlete at the 1960 Winter Olympics.

[1][2] Grishin was the first to break the 40 second barrier on the 500 m, skating 39.6 in an unofficial test race in Squaw Valley in 1960, just after the Winter Olympic Games at the same location.

Three years later, on 27–28 January 1963, he set officially ratified world records 39.6 and 39.5 at the Medeu track.

Over the course of his career Grishin set seven world records; the 1:22.8 time of the 1000 m lasted 12 years.