Richard Gilmour was a Scottish-born prelate of the Roman Catholic Church. He served as bishop of the Diocese of Cleveland in Ohio from 1872 until his death in 1891.

The Diocese of Cleveland is a Latin Church ecclesiastical territory, or diocese, of the Catholic Church in northeastern Ohio in the United States. As of September 2020, the bishop is Edward Malesic. The Cathedral of St. John the Evangelist, located in Cleveland, is the mother church of the diocese.