Robert Fleming may refer to:
Robert Fleming (author), American journalist and writer of mysteries, horror, and erotic fiction
Robert Fleming (composer) (1921–1976), Canadian composer
Robert Fleming (cricketer) (born 1953), English cricketer
Robert Fleming (financier) (1845–1933), Scottish financier and founder of the merchant bank Robert Fleming & Co
Robert Fleming (footballer) (1860–?), Scottish footballer
Robert Fleming (New York politician), American politician, member of the New York State Assembly (1817–1818; 1834)
Robert Fleming (Canadian politician) (1918–1985), Canadian politician in the Yukon
Robert Fleming the elder (1630–1694), Scottish Calvinist minister and theologian
Robert Fleming the younger (c. 1660–1716), Scottish Presbyterian minister, son of Robert Fleming the elder
Robert Alexander Fleming (1862–1947), Scottish pathologist and medical author
Robert D. Fleming (1903–1994), Pennsylvania politician
Robert E. Fleming (born 1936), American literary critic and university professor
Robert John Fleming (1907–1984), American soldier and governor of the Panama Canal Zone
Robert John Fleming (Canadian politician) (1854–1925), mayor of Toronto, Canada
Robert Loren Fleming (born 1956), American comic book writer
Rob Fleming (born 1971), Canadian politician
Bob Fleming, fictional character in the British comedy sketch show The Fast Show