Grasby (also spelled Grassby) is an English language surname of toponymic (habitation/location) origin.
Notable people with the surname include:
Marion Grasby (born 1982), Australian cook and food entrepreneur of Anglo-Celtic Australian and Thai Australian heritage. William Grasby (1859–1930), Australian agricultural journalist and educationist Al Grassby (1926–2005), Australian politician Bertram Grassby (1880–1953), English silent movie actor Ellnor Grassby (born 1937), Australian politician