Sir Robert Gunning, 1st Baronet GCB (8 June 1731 – 22 September 1816) was a British diplomat. He served as the British minister in Denmark 1765–1771, in Prussia in 1771 and in Russia 1772–1776. Gunning was appointed a Knight Companion of the Order of the Bath on 9 July 1773 and the first Baronet of Eltham in the County of Kent on 27 October 1778.