Grímsson is a surname of Icelandic origin, meaning son of Grímur.^{[citation needed]} In Icelandic names, the name is not strictly a surname, but a patronymic. The name refers to:

• Grímur Grímsson, member of the Icelandic parliament
• Lárus Halldór Grímsson (b. 1954), Icelandic musician, composer, and conductor
• Ólafur Ragnar Grímsson (b. 1943), Icelandic politician; President of Iceland since 1996
• Stefán Hörður Grímsson (1919–2002), Icelandic poet