Alexander Gibson may refer to:
Alexander Gibson, Lord Durie I (died 1644), Scottish judge
Alexander Gibson, Lord Durie II (died 1656), Scottish judge, son of Alexander Gibson, Lord Durie I
Alexander Gibson (botanist) (1800–1867), botanist and forester in India
Alexander Craig Gibson (1813–1874), folklorist around Coniston, Cumbria
Alexander Gibson (conductor) (1926–1995), Scottish conductor and music director
Alexander Gibson (industrialist) (1819–1913), Canadian industrialist
Alexander Gibson (politician) (1852–1920), Canadian politician
Alexander George Gibson (1875–1950), English physician
Alexander James Gibson (1876–1960), professor of engineering at University of Queensland in Australia
