Peter Sundstrom played junior hockey in his home country Sweden with his twin brother Patrik and represented his country at the World Junior Championships in 1981 where the team won a gold medal. This year also saw Sundstrom drafted by the Rangers.
The 1981-82 season saw Sundstrom play in Sweden as well as being a part of the World Championships this year and next. He made his NHL debut in the 1983-84 season with the Rangers and saw his first action in the Stanley Cup playoffs. He played in New York for two more seasons before leaving the team to play in Sweden for the 1986-87 season. The Rangers then traded Sundstrom to the Capitals where he spent two seasons.
Sundstrom was dealt one last time to the Devils in 1989-90 where he finished his NHL career. The next year, Sundstrom headed back to his home country to play for the next five years before hanging them up in 1994-95.