Duncan is a town in Greenlee County, Arizona, United States. As of the 2010 census, the population of the town was 696. In 2018 the estimated population was 789. Duncan is in the Gila River valley, four miles west of the Arizona–New Mexico border. The town limits are on both sides of the Gila River, but the primary portion of the town and the entire downtown area lies on the south side of the river.