Since 1992 he has been a member of the Svend Asmussen Quartet and he has founded his own Jacob Fischer Trio where he plays alongside Hugo Rasmussen on bass and Janus Templeton on drums. He is a member of Christina von Bülow's trio and the Kristian Jørgensens Quartet.
Jacob Fischer started to play at the age of 14 and Wes Montgomery, B.B. King and Django Reinhardt were among his first inspirations. Fischer had his debut at the age of 17 when he played at the Copenhagen Jazz Festival. Around the same time he also won a competition arranged by national Danish newspaper Berlingske Tidende with a band which included Chris Minh Doky on bass and Nikolaj Hess on piano. This led to the first engagement at the legendary jazz club Jazzhus Montmartre in Copenhagen.
In 1992 he became a member of Svend Asmussen quartet. Since then he has played in numerous ensembles and with the entire Danish jazz elite, including Allan Botschinsky, Jesper Thilo, Finn Ziegler, Bob Rockwell and Radioens bigband. He has also formed duos with the guitarist Doug Raney and the bassists Hugo Rasmussen and Mads Vinding. He has also played with international jazz musicians such as Toots Thielemans, Art Farmer, Lee Konitz, Gary Bartz, John Abercrombie, Scott Hamilton, Adam Nussbaum, Putte Wickman, Jan Allan and Jerry Bergonzi.
- 1992 JASA-prisen
- 1987 Sørens Penge
- 1996 Ben Webster Prize
- 1998 Palæbars jazzpris
- 2003 Jazzpris Silkeborg
- Duets with Kristian Jorgensen (Music Mecca, 2000)
- Over the Rainbow, with Mads Vinding (Cope, 2002)
- Jacob Fischer Trio feat. Svend Asmussen, (Gateway, 2008)
- Blues, (Gateway, 2010)
- Django, (Gateway, 2010)
- Guitarist (Arbors, 2012)
- Black Orpheus, (Venus, 2013)
- My Romance, (Venus, 2014)
- X-MAS Friends, (Gateway, 2013)
- In New York City, (Arbors, 2015)