Sigmund has continuously released albums since 1975. These are the standard original covers for his Norwegian albums, both solo albums and collaborations. Re-editions or foreign editions may have different artwork.
- 2023 – Kjenslevev
- 2021 – In Concert
- 2020 – The sound of Telemark
- 2019 – Songs for harmonica
- 2018 – Bønn for drømmen
- 2016 – Concerto
- 2015 – Tradition
- 2014 – Harmonica Hits
- 2012 – Classical Harmonica
- 2010 – harmOrgan (with Iver Kleive)
- 2007 – Grieg Album
- 2005 – PhilHarmonica
- 2004 – Here, There and Everywhere
- 2003 – Over the Rainbow
- 2001 – Vi på Langedrag
- 2000 – Innunder jul (with Iver Kleive)
- 1998 – Harmonica Album
- 1996 – I godt lag (2CD compilation)
- 1995 – Til Telemark
- 1993 – Siesta
- 1991 – Nattønsker (compilation)
- 1990 – Nordisk natt
- 1988 – Aria
- 1988 – Sigmund Groven (compilation)
- 1986 – Marit og trollstenen (with Ove Røsbak)
- 1985 – Colour slides
- 1983 – Songar utan ord (with Henning Sommerro)
- 1981 – Lævandes dikt (with Ove Røsbak and Iver Kleive)
- 1981 – Kom sol på alle mine berg (with Geirr Lystrup)
- 1981 – Musikken inni oss (with Arve Tellefsen)
- 1979 – Motlys
- 1977 – Musikk for en lang natt (with Ketil Bjørnstad)
- 1976 – Music for two Harmonicas (with Tommy Reilly)
- 1975 – Så spiller vi harmonica
Many of the CDs are available to buy from Grappa (worldwide shipping possible).