Brim was founded in 1998 and operated at that time under the name Tjaldur ehf. This was a division of the established company founded by Kristjan Gudmundsson and his sons, Hjalmar and Gudmundur, in the town of Rif on the Icelandic west coast. Gudmundur had moved to Reykjavík by then and was managing the branch based in the city. From the start of the company, the main office has been situated at Tryggvagata 11 in Reykjavik, until November 2007 when it moved to Braedraborgarstigur 16. In the year 2005 the name of the company was changed into Brim and it is safe to say it has found its place amongst the leading fishing companies in Iceland.

At first the company managed one longliner, Tjaldur SH 270,  and had around 20 members of staff. The catch was brought fresh to the Icelandic fishing markets and frozen for the foreign markets. In 1999  Brim bought another fishing company which enabled it to manage two freezer stern trawlers that operated solely in the shrimp fisheries.In 2003, the company decided to cease further catching of shrimp.  Subsequently the freezer stern trawler Gudmundur i Nesi RE 13 was purchased at the beginning of year 2004. Guðmundur i Nesi is a vessel that specialises in fishing of Greenland halibut.

In 2004 the company purchased the Fishery of Akureyri  (ÚA), in partnership with KG fishery at Rif which owns a 20% share. Consequently  ÚA  was merged with Brim in the year 2005. Today Brim plays a significant part in the Icelandic fishing industry. It manages the freezer trawler Brimnes 27 and Gudmundur i Nesi RE 13,  the wetfish trawlers Kaldbakur EA 1, Arbakur RE 205, Kleifaberg OF 2 and the Danish Seine vessel Solborg RE 270.