Hans Abrahamsen started by playing the French horn, but even at a very young age he showed a remarkable talent for composition. In 1969 he began to study French horn at the Royal Danish Academy of Music in Copenhagen, but already in 1970-71 he had his first lessons in composition with Niels Viggo Bentzon. In 1971 he studied composition at the Royal Academy of Music in Århus where he was taught composition by Pelle Gudmundsen-Holmgreen. He has also studied with Per Nørgård and György Ligeti. From 1975-81 he went back to Copenhagen to study music history and music theory. In his early career Hans Abrahamsen was a key figure in the Danish New Simplicity movement which reacted against the complexities of the Darmstadt school. Despite the small scale and brevity of many of his works, his music often has an epic quality, creating the impression that behind the scarcity of material lie expansive concepts and dense thought.

Since 1995 Abrahamsen has himself taught instrumentation and composition at the Academy of music in Copenhagen. He has received among other honors Carl Nielsen and Anne Marie Carl-Nielsens Hæderspris (1989) and the Wilhelm Hansen Prize (1998).