The winner of the 1980 Conn Smythe trophy as NHL Playoff MVP was Bryan Trottier of the New York Islanders. The Islanders won the first of 4 consecutive Stanley Cups in 1980.
The Islanders led by hall of famers Denis Potvin, Billy Smith, Mike Bossy, Bryan Trottier and head coach Al Arbor beat the Philadelphia Flyers 4 games to 2. The Isles clinched the cup in game 6 as Bobby Nystrom scored the cup winner in overtime to give the Islanders a 5-4 win.
Trottier was number 6 in scoring for the regular season with 42 goals and 62 assist for 104 points. Strangely none of the Islanders made the all NHL 1st or 2nd teams for the 1979-80 season.
Here is a link to Bryan Trottier's memories of the 1980 Finals.