In 1969, KFÍ won the Vesturland's group and was slated to face Þór Akureyri, which won the Norðurland's group, in a game for the national championship.

[6][7] In 2016 KFÍ merged into Íþróttafélagið Vestri and became its basketball sub-division.

[10] In July 2021, Dimitris Zacharias was hired as the head coach of the team.

[11] In end of November, Zacharias resigned[12] and was replaced by former coach Pétur Már Sigurðsson.

In June 2022, the board decided not to register the team for the next season competition.