Capon Bridge is a town located in eastern Hampshire County, West Virginia, USA, along the Northwestern Turnpike, approximately twenty miles west of Winchester, Virginia. The population was 355 at the 2010 census, 200 of which live within the town limits. Originally known as Glencoe, Capon Bridge was incorporated in 1902 by the Hampshire County Circuit Court. It is named because of the construction of the bridge over the Cacapon River at that place, the name of the river being derived from the Shawnee Cape-cape-de-hon, meaning "river of medicine water".