Ásgrímur Magnússon (died 1679) was a poet and farmer in North Iceland. He farmed for many years at Höfði in Höfðaströnd but eventually moved to Kvíabekkur in Ólafsfjörður, where he died.
Ásgrímur Magnússon's first wife was Erlendsdóttir, sister of fellow poet Guðmundur Erlendsson of Fell in Sléttuhlíð. died as a young woman. They had at least one child, (c. 1626–after 1703). After 's death, Ásgrímur married . Their children were (1636–1706), Herdís (1638–after 1709) and Erlendur (c. 1644–after 1705).
Ásgrímur composed rímur poetry and is believed to have co-composed in c. 1640 with his brother-in-law . Ásgrímur is a speaker in the poem, in which Grýla visits his home at at Christmas and threatens to steal his young daughters, Valka (Valgerður) and Herdís. His have survived in several manuscripts, including AM 142 8vo, which is a copy of Ásgrímur's autograph manuscript.