People with the surname Maxim include;

• Alexandru Maxim (born 1990), Romanian football player
• Cristian Maxim (born 2003), Romanian football player
• Florin Maxim (born 1981), Romanian football player
• Hiram Maxim (1840–1916), inventor of the Maxim Gun, the first machine gun
• Hiram Percy Maxim (1869–1936), founder of the American Radio Relay League
• Hiram Stevens Maxim (1840–1916), inventor and firearm designer
• Hudson Maxim (1853–1927), a U.S. inventor and chemist; brother of Hiram Maxim and uncle of Hiram Percy Maxim
• Joey Maxim (1922–2001), American boxer and one-time Light Heavyweight champion of the world
• John Maxim (1925–1990), English actor
• Marinela Maxim (born 1955), Romanian rower