Duncan is a town in Greenlee County, Arizona, United States. According to the 2010 census, the population of the town is 696. Duncan is at the juncture of the Gila River and the Arizona-New Mexico state border. Duncan lies on both sides of the Gila, although the primary portion of the town and the entire downtown area lie on the south side of the river. Duncan was founded in the mid 19th century, and the land was added to the United States as a part of the Mexican Cession.