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 (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), 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