Olsen captained the Danish team that qualified for the 1984 European Championship; Denmark's first international tournament participation since the 1972 Olympics. Denmark reached the semi-finals, before being eliminated by Spain on penalty shootout. In October 1985, Olsen became the second Dane, after Per Røntved, to play 75 national team matches. He captained Denmark at the 1986 World Cup, Denmark's first World Cup participation, which ended in a second round defeat to Spain. Olsen's most noticeable effort at the tournament came in the 2–0 group stage win against West Germany. He took the ball from his own half and made an irresistible dribbling run that was only stopped by a foul in the West German penalty area, with Jesper Olsen scoring the 1–0 goal on the resulting penalty kick. Olsen was identified as one of the overall top performers at the World Cup, and he was subsequently named 1986 Danish "Player of the Year".