Duncan is a town in Greenlee County, Arizona, United States. According to 2006 Census Bureau estimates, the population of the town is 713. It is part of the Safford Micropolitan Statistical Area. 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.