Augustus Frederick Adolphus Greeves (7 September 1806 – 23 May 1874) was a Mayor of Melbourne and Member of Parliament in Melbourne, Australia. Greeves was born in Knaresborough, Yorkshire, England and emigrated to the Port Phillip District in New South Wales in 1840. He was one of the first medical men to arrive in Melbourne. He was a surgeon, publican and local councillor and was the Mayor of the City of Melbourne between 1849 and 1850. He was also, for a short time, the editor of the Port Phillip Gazette and the Melbourne Morning Herald. He was a founding member of Manchester Unity I.O.O.F. in Victoria.