Before the introduction of the World Cup, Mjøen achieved a second place in the slalom of the 3-Tre race in Madonna di Campiglio on February 12, 1966. At the 1966 World Cup in Portillo , ninth place in the slalom was his best result. In the pre-Olympic slalom on February 18, 1967 in Chamrousse , he won ahead of Guy Périllat .
His best result in the Ski World Cup , which was held for the first time in 1967, is a second place, placed on January 14, 1968 at the Lauberhorn Slalom in Wengen . In addition, there was a third place in the slalom in Oslo in February 1968 and six further placements among the top ten. At the 1968 Winter Olympics , Mjøen was tenth after the first run of the slalom and took the lead in the second run. As it turned out a few minutes later, Mjøen had missed two goals in the thick fog and the alleged Olympic champion had to be disqualified.