General Alexander Montgomery (c.1721—1785) was an Irish MP for County Monaghan, Ireland. His father was John Montgomery (died 1733) of Ballyleck, County Monaghan (M.P. for County Monaghan and second son of Colonel Alexander Montgomery (1667–1722)). John had succeeded his father to the Ballyleck Estate when his elder brother Thomas was disinherited for marrying an Englishwoman.