 He was named Auxiliary Bishop of San Antonio on June 30, 1981 by Pope John Paul II, with the titular see of Equilium.The Pope appointed him the first bishop of the newly created Diocese of Victoria, Texas on April 13, 1982.In 1989, Grahmann was appointed Coadjutor Bishop of the Diocese of Dallas, Texas, and he became Bishop of Dallas on July 14, 1990.