Jan Bertil Allan (born 7 November 1934 in Falun) is a Swedish jazz trumpeter and composer. He is the winner of a Grammis Award, the Swedish equivalent of the Grammys. He has also composed for several films such as The Adventures of Picasso (1978), Sopor (1981) and Trollkarlen (1999).
Allan began his career in 1951 as a pianist; after moving to , he changed to the trumpet as his main instrument. At this time he played in Carl-Henrik Norin's orchestra. From 1954–55 he worked with Lars Gullin and Rolf Billberg and from 1955–59 with Carl-Henrik Norin. At the same time he earned a PhD in physics.
Despite his small number of records, Allan is among the most important modern jazz musicians in Sweden. From 1960–63 he led a quintet with Billberg. Over the course of the 1960s, he worked with Arne Domnérus, Georg Riedel, and Bengt Hallberg, among others. From 1968 to 1975 he was a member of the Swedish Radio Jazz Group. His album Jan Allan -70, which featured Rolf Ericson, Nils Lindberg, Bobo Stenson, Jon Christensen, and Rune Gustafson, won a Grammis Award for Jazz of the Year in 1970. Allan played with the same group and Georg Riedel on the trio-album Sweet And Loverly. His 1998 album Software stands in strong affinity with the West Coast Jazz of Gerry Mulligan and Stan Getz.