Burney is a surname. Notable people with the surname include:
Ansar Burney (born 1956), Pakistani human rights activist
Cecil Burney (1858–1929), British admiral
Charles Burney (disambiguation), several people
Christopher Burney (1917–1980), British spy during World War II.
Dennistoun Burney (1888–1968), British engineer and inventor
Edward Francis Burney (1760–1848), English artist and illustrator
Frances Burney (1752–1840), English novelist and diarist
Henry Burney (1792–1845), British agent and ambassador of the East India Company (19th century)
James Burney (1750–1821), British admiral
Sarah Burney (1772–1844), novelist, known as S.H. Burney
S. M. H. Burney (Sayed Muzaffar Hussain Burney, 1923–2014), Indian civil servant
Venetia Burney (1918–2009), namer of the dwarf planet Pluto
