George Brown played for the Elmwood Millionaires of the Western Junior Hockey League for two years, winning the Memorial Cup championship in 1931. He then joined the Winnipeg Monarchs in 1932, where the team advanced to the Memorial Cup before losing to the Sudbury Wolves. Brown also played for the Montreal Royals before joining the Verdun Maple Leafs in 1934-35. In his second year with Verdun, Brown potted 19 goals and 42 points to lead the MCHL in scoring.
In 1936-37, Brown began a three-year NHL career with the Montreal Canadiens. In his first year he played in 27 games, scoring six goals and ten points. The following year he appeared in 34 games, scoring a goal and four assists. In 1938-39, he played another 18 games for Montreal. In 79 NHL games, he scored six times while gathering 28 points. He continued to play hockey for another four years, retiring after the 1942-43 season with the Montreal Canadiens of the QSHL.