Anderson was born in Vancouver and raised in Burnaby, British Columbia. His father, Magnus, is the son of a Norwegian immigrant, and his mother, Anne, is of Ukrainian origin. He has two brothers (Allan and David) and a sister (Pam). As a young child, Anderson did not enjoy the game of ice hockey. His first ever goal was in his own net. However, as he grew older, and developed his skills, Anderson’s love of the game increased over time. As a youth, he and teammate Ken Berry played in the 1972 Quebec International Pee-Wee Hockey Tournament with a minor ice hockey team from Burnaby.

In the 1979 NHL Entry Draft Anderson was drafted 69th overall by the Edmonton Oilers of the National Hockey League (NHL). He opted to play for Team Canada during the 1980 Winter Olympics in Lake Placid. Father David Bauer, in charge of the national team program, accepted Anderson. Father Bauer’s influence on Anderson was significant as he would cite him as a major reason for his later success. The team toured the world playing different opponents in preparation for the Olympics. The practice Anderson received during this time helped “greatly improve” his skills. Anderson scored four points in six games during the tournament.

Anderson was chosen to participate in the 1984 Canada Cup. The roster included eight of Anderson’s teammates from the Edmonton Oilers. Canada advanced to the finals and defeated Sweden 2–0 in a best of three series to win the Cup. Anderson scored five points during the tournament. The 1987 Canada Cup also saw Anderson participate. Once more, Canada reached the finals, but this time they were up against the Soviet Union. The finals required all three games as Canada defeated the Soviet Union. All three games needed overtime and had a final score of 6–5. Anderson recorded three points during the tournament.

In 1989, Anderson played at the Ice Hockey World Championships for the first time. With four points in six games, Anderson helped Canada win the silver medal, as the Soviets took home the gold. Three years later, Anderson made his second and final appearance at the World Ice Hockey Championships, this time in Czechoslovakia. Canada was eliminated by Finland in the quarterfinals by a score of 4–3. Anderson registered three points during the tournament.

Anderson was inducted into the Hockey Hall of Fame on November 10, 2008 in the players category. His jersey number 9 was retired on January 18, 2009, by the Oilers, before a game against the Phoenix Coyotes. The date for Anderson’s number retirement was specifically selected because his former Oilers teammates, Wayne Gretzky and Grant Fuhr, were serving as the Coyotes’ head coach and goaltending coach respectively at the time.

Growing up, Anderson played hockey with his childhood friends. Anderson’s hockey idol was not Canadian; instead, his favourite player was Russian Alexander Yakushev, whom he had watched play during the 1972 Summit Series. Glenn eventually produced the one hour documentary “To Russia With Love”, released in September 2012, about the way Russia changed the Canadian ice hockey game.