George McAvoy played with the Edmonton Athletic Club for two years and helped the team to the Memorial Cup in 1949. He then headed east to play for the Laval Nationale and the Montreal Junior Canadiens of the QJHL in 1950 and 1951.
McAvoy made brief stops in Halifax and Boston before joining the Penticton Vees where he played for three years, leading them to two Allan Cup appearances. In 1955 McAvoy and the Vees represented Canada at the World Championships which was by far the greatest honour of his career. He responded with two goals and four points in eight games. He is perhaps best remembered for a crushing hit on Russia's Vsevolod Bobrov, who was not only that country's best hockey player, but also one of its elite soccer stars of that era. Bobrov was skating fast out of his own zone with the puck heading into the neutral zone. His mistake was having his head down, looking at the puck. McAvoy lined him up and walloped him so hard that media scribes in attendance say Bobrov came close to hitting his head on the timer that hovered above centre ice. Bobrov was unconscious before he hit the ice. He lay motionless on the ice for several minutes before being carried off on a stretcher. He did not return. McAvoy's crushing bodycheck did not go unnoticed. A Montreal Canadiens scout was in attendance and readily offered McAvoy a contract after the game, which the rugged defender accepted without hesitation.
Although McAvoy never played a regular season game in the NHL, he was called upon to play for the Montreal Canadiens for four playoff games in 1955 playing with stars such as Maurice Richard, Doug Harvey and Jacques Plante.
McAvoy was certainly well travelled during his pro hockey career. He suited up for Providence of the AHL for three years and then spent two seasons in Cleveland with the Barons. He then wound up with the Calgary Stampeders for three years before sitting out the 1963-64 campaign. He returned in 1964 to play with the Edmonton Eskimos in the X-Games and the WCSHL, retiring after the 1965-66 season.