He had three seasons of junior with the Toronto Young Rangers and Brantford Lions and one year split between senior hockey and professional when his career was interrupted by military service in 1943. He returned to the ice for the 1944-45 season and led his Senior loop with 28 goals that year.
Simpson rejoined the Indianapolis Capitals in 1945-46, with whom he had spent a short time with before his military duties, and enjoyed a solid season, scoring 21 goals. The following year he posted All-Star numbers when he notched 42 goals and 78 points in 54 games. His impressive production earned him a trip to the big leagues during that campaign.
Simpson played six games with the Detroit Red Wings and managed 1 assist. He also appeared in a single playoff game for Detroit but did not register a point.
In the 1948-49 season Simpson built on his success with Indianapolis and upped his totals to 48 goals and 110 points and was again named an All-Star. His effectiveness again captured the attention of the Red Wings who summoned him for a playoff contest that spring. It would prove to be Simpson's last NHL appearance.
Simpson spent one more year with Indianapolis but his offensive output dipped dramatically when he only posted 46 points in 52 games. He then moved on to the St. Louis Flyers in 1949 and played the final three years of his career with them retiring after the 1952 season.