Jessop is a surname. Notable people with the surname include:
- Bob Jessop (born 1946), British Marxist theoretician
- Carolyn Jessop (born 1968), American author
- Charles Minshall Jessop (1861–1939), mathematician
- Christine Jessop (1974–1984), Canadian child murdered in 1984
- Clytie Jessop (1929–2017), British actress
- Craig Jessop (born 1949), American academic
- Elisha Jessop (1843–1918), Canadian doctor and politician
- Flora Jessop , American social activist
- Gilbert Jessop (1874–1955), English cricketer
- Gilbert Jessop (cricketer, born 1906), his son, also an English cricketer
- Graham Jessop (1957–2012), English marine archaeologist
- Greg Jessop, fictional character from the British soap opera EastEnders
- Job Dean Jessop (1926–2001), American thoroughbred jockey
- Keith Jessop (1933–2010), English salvage diver
- Peter Jessop (born 1964), American film actor
- Violet Jessop (1887–1971), Argentine nurse and ocean liner stewardess who survived the sinking of the RMS Titanic in 1912
- William Jessop (disambiguation), multiple people
- Willie Jessop, leader of Fundamentalist Church of Jesus Christ of Latter Day Saints