A first special mention was given to him at the Lauberhorn Slalom in Wengen on January 10, 1960, when he was given start no. 69 (exactly 3 seconds behind the winner Hias Leitner ) was sixth.
A first major success dates back to January 10, 1965, when he (again) took 3rd place in the Lauberhorn Slalom. Grahn won the slalom in the first snow criterion in Val-d'Isère in both 1965 and 1966 , although his first victory (after a previous disqualification, whereby Jean-Claude Killy was initially considered the winner) was only certain a few hours later. In 1966 he was also second in the combination. Grahn won his first World Cup points on January 22nd, 1967 when he finished second behind Jean-Claude Killy in the slalom in Kitzbühel . After that, he only placed himself twice in the World Cup prizes as slalom tenth. From 1961 to 1971 he was Swedish champion seven times - three times in slalom, three times in giant slalom and once in downhill. After his skiing career, Grahn worked as a sports teacher.