Trygve Seim is a Norwegian jazz saxophonist. Born in Oslo, Seim started to play the saxophone in 1985 after hearing Jan Garbarek's CD eventyr. He started studying jazz music at the Trondheim Conservatory of Music in 1990.

In 1991, he and pianist Christian Wallumrød founded the group Airamero with Johannes Eick on bass and Per Oddvar Johansen on drums. The group made one record, Airamero in 1994. It also undertook several concert tours in Scandinavia and Germany.

Trygve became a member of Jon Balke's group Oslo 13 in 1992, and took over the joint leadership of the group in 1994 with Morten Halle and Torbjørn Sunde. The group is now called 1300 Oslo.

Seim is also a member fo jazz quartet The Source with Øyvind Brække, Ingebrigt Flaten and Per Oddvar Johansen. They have made five records and played several concert tours all over Europe and Russia.

He has also played with Edward Vesala and Kenny Wheeler.

Seim's CD release Different Rivers on the record label ECM in 2001 received good reviews all over the world, winning the German Record Critics Prize, the Preis der Deutsche Schallplattenkritik. Since then, he has released several records with ECM.

He has, more recently, composed music for classical musicians, especially Norwegian opera singer Anne-Lise Berntsen, and such as his new work Between Voice and Presence for the Trio Mediaeval. For the 2006 Voss Jazz Festival, he has written a full-length commissioned concert, Reiser.