Cleaver is a surname. Notable people with the surname include:
Cleaver Bunton (1902–1999), Australian politician
Billy Cleaver (1921–2003), Welsh rugby union player
Eldridge Cleaver (1935–1998), American writer and political activist
Emanuel Cleaver (born 1944), U.S. Representative for Missouri and United Methodist pastor
Euseby Cleaver (1746–1819), Anglican Archbishop of Dublin
Gerald Cleaver (musician) (born 1963), African-American jazz drummer
Gerald B. Cleaver, physics associate professor at Baylor University
Gordon Cleaver (died 1994), British Second World War fighter ace and skier
Harry Cleaver (born 1944), economics associate professor at the University of Texas at Austin
Hughes Cleaver (1892–1980), Canadian politician
Kathleen Neal Cleaver (born 1945), American professor of law
Naomi Cleaver (born 1967), British design consultant and interior designer
Richard Cleaver (1917-2006), Australian politician
Solomon Cleaver (1855–1939), Canadian minister and storyteller
Sue Cleaver (born 1965), English actress
Val Cleaver (1917-1977), British rocket engineer
William Cleaver (1742–1815), English bishop and academic
