Guttormsson is a Nordic surname. Notable people with this surname include:
Bård Guttormsson (c. 1150–1194), medieval Norwegian nobleman Jón Guttormsson Skráveifa (died 1361), governor of Iceland (1357–1360) Andras Guttormsson (c. 1490–1544), First Minister of the Faroe Islands (1531–1544) Ísak Guttormsson, First Minister of the Faroe Islands (1583–1588) Guttormur J. Guttormsson (1878-1966), Icelandic Canadian playwright and poet Hjörleifur Guttormsson (born 1935), Icelandic politician