Kurri started his ice hockey career in the junior team of Jokerit. Already in age of 17, he played in Jokerit team adults. He also played for Finnish Junior National Team in 1978, 1979, and 1980. He played on the Olympic Finland team in 1980.
In 1980 he was invited to play for Edmonton Oilers in Canada. There he played with Wayne Gretzky for 8 seasons until Gretzky moved to Los Angeles. They became famous. Oilers won Stanley Cup 1984, 1985, 1987, 1988, and 1990. Later Kurri played for Los Angeles Kings, New York Rangers, Mighty Ducks of Anaheim and Colorado Avalanche.
During his career Kurri made 600 goals in NHL.
Because Kurri was most years continuing his NHL term in North America in Stanley Cup playoffs, he could not play for Finland National tesm very often. However he was in Olympic Games in Nagano 1998, and got a bronze medal.