Robert Gunning may refer to:

• Sir Robert Gunning, 1st Baronet (1731–1816), British diplomat
• Robert C. Gunning, professor of mathematics at Princeton University
• Robert Halliday Gunning (1818–1900), Scottish physician
• Robert Gunning, American businessman, creator of the Gunning fog index of readability
• Robert Gunning, musician, guitarist for The Infected
• Sir Robert Gunning, 3rd Baronet (1795–1862), of the Gunning baronets, MP for Northampton
• Sir Robert Charles Gunning, 8th Baronet (1901–1989), of the Gunning baronets

• Gunning (disambiguation)