Burney is a surname. Notable people with the surname include:
Amari Burney (born 2000), American football player Ansar Burney (born 1956), Pakistani-Arab human rights activist Cecil Burney (1858–1929), British admiral Charles Burney (disambiguation), several people Christopher Burney (1917–1980), British spy during World War II Clarence A. Burney (1876–1933), Justice of the Supreme Court of Missouri 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, ambassador of the East India Company James Burney (1750–1821), British admiral Linda Burney (born 1957), Australian politician 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