Duncan is a town in Greenlee County, Arizona, United States. As of the 2010 census, the population of the town was 696. In 2015 the estimated population was 799.Duncan is in the Gila River valley, 4 miles west of the Arizona-New Mexico border. The town limits are on both sides of the Gila, but 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. The town of Duncan has been destroyed twice by flood and once by fire.The town and area are primarily populated by ranchers and miners. Surrounding smaller towns such as Franklin and York in Arizona and Virden, New Mexico, use Duncan public works and public schools.