Mārtiņš Grīnbergs learned the basics of playing the bassoon from 1991 to 1996 in the Emilis Melngailis Liepāja Music College under Jānis Dreiže, also periodically improving under Dzintars Jurgelaitis. Mārtiņš continued his studies in the Jāzeps Vītols Latvian Academy of Music under professor Andris Arnicāns (1996–2000).
From 1995 to 2009 Mārtiņš performed with the Liepāja Symphony Orchestra; since 2002 he is the bassoonist of the Latvian National Opera and Ballet Orchestra and since 2006 he works in Sinfonietta Rīga as well. Mārtiņš has also played in several youth orchestras.
In his free time Mārtiņš actively does sports – he does long-distance running, and has already finished twelve half marathons and two marathons (Belfast and Berlin, both in 2014). Mārtiņš also likes beer and enjoys gastronomical adventures.