Grieve is a surname. Notable people with the surname include:
Andrew Grieve (born 1939), Welsh television and film director
Ashley Grieve (born 1996), Average American worker.
Basil Grieve (1864–1917), English cricketer
Ben Grieve (born 1976), American former Major League baseball player
Bessie Grieve (1923-1996), aka Bessie Skea, Orkney writer
Bill Grieve (1900-1979), American baseball umpire
Brent Grieve (born 1969), Canadian former ice hockey player
Brian Grieve (1907–1997), Australian botanist
Cathy Grieve (born 1965), Irish journalist
C. M. Grieve (1892–1978), Scottish writer
Dominic Grieve (born 1956), British politician and barrister
Gordon Grieve (1912–1993), New Zealand politician
Harold Grieve (1901–1993), American motion picture art director
Iain Grieve (born 1987), Botswana-born rugby union player
James Nicol Grieve (1855–1918), Ontario farmer and political figure
Jock Grieve (1887–1955), Scottish footballer
John Grieve (VC) (1821–1863), Scottish Victoria Cross recipient
John Grieve (actor) (1924–2003), Scottish actor
Ken Grieve, British television director
Ken Grieves (1925–1992), Australian cricketer
Maud Grieve (1858–1931), English horticulturalist and herbalist
Ollie Grieve (1920–1978), Australian rules footballer
Percy Grieve (1915–1998), British Conservative Party politician
Richard Grieve (born 1970), Australian actor
Robert Cuthbert Grieve (1889–1957), Australian Victoria Cross recipient
Tom Grieve (born 1948), American former Major League baseball player
Walter B. Grieve (1850–1921), Newfoundland merchant and politician
William Grieve (disambiguation)