Grimstad is a Norwegian surname. Notable people with the surname include:
Birgitte Grimstad (born 1935), Danish-born Norwegian musician
Carl M. Grimstad (1856–1940), American politician
Carl-Erik Grimstad (born 1952), Norwegian politician
Edvard Grimstad (1933–2014), Norwegian politician
Gudmund Grimstad (1898–1970), Norwegian wrestler
Lars Joachim Grimstad (born 1972), Norwegian football midfielder
May-Helen Molvær Grimstad (born 1968), Norwegian politician
Oskar Jarle Grimstad (born 1954), Norwegian politician
Per Ø. Grimstad (born 1934), Norwegian businessperson, diplomat and politician
Renate Grimstad (born 1997), Norwegian golfer