Griswold went to school at St. Paul's School in Concord, New Hampshire. He earned an A.B. in English literature from Harvard College (1959). He attended the General Theological Seminary and earned his B.A. and M.A, in theology from Oriel College, Oxford University (1962, 1966). Griswold became a priest in 1963. He became a priest in Pennsylvania. He worked at three churches there. Frank Griswold was the bishop of Chicago from 1987 until he became presiding bishop in 1997.
Griswold is a member of the Joint Standing Committee of the Primates of the Anglican Communion and the Anglican Consultative Council. He was co-chair of the Anglican-Roman Catholic International Commission from 1998 to 2003. He was a member of the standing committee for the 1998 Lambeth Conference. He has also served on diocesan, national and international committees for liturgy, worship and ecumenism. He is also a member of The Fellowship of Saint John.
His term as presiding bishop ended on November first 2006. He was replaced by the Rt. Reverand Katharine Jefferts Schori. She was elected by the General Convention of the Episcopal Church in the United States of America.