According to the Book of Settlements, Steingrimur Trolli settled the Steingrimsfjordur area and lived at farm Trollatunga.  It was a parsonage until 1886 and a church site until 1909.  The church owned the right to a part of the driftwood of five farms and beached whales of ten farms.

An ancient church bell from Trollatunga is kept in the National Museum.  The last Reverend, Halldor Jonsson, and two brothers founded a reading society for the advancement of culture in the benefice with good results.