The Gunning Baronetcy, of Eltham in the County of Kent, is a title in the Baronetage of Great Britain. It was created on 3 September 1778 for Robert Gunning, Minister Plenipotentiary to Berlin and St Petersburg. The second Baronet was Member of Parliament for Wigan, Hastings and East Grinstead while the third Baronet briefly represented Northampton. The seventh Baronet was a Brigadier-General in the British Army.
Orlando George Gunning, grandson of Major John Gunning, sixth son of the second Baronet, was also a Brigadier-General in the Army. The 17th century clergyman Peter Gunning was another member of the family.
The family seat from 1782 to 1888 was Horton House, Horton, Northamptonshire.