Playing for Malmö FF, his career there was successful, becoming Swedish champion in 1974, 1975 and 1977, as well as runner-up in the European Cup 1979 (a 0–1 defeat to Nottingham Forest). He represented the Swedish national team at the 1974 and 1978 World Cups as well as on a number of other occasions. However, many remember him for missing a penalty kick against Poland at the 1974 World Cup. For some time, Tapper was first team coach at Malmö FF, he later resigned from that role to become youth talent coach.