Henry Glemham (Glenham) (c.1603 – 17 January 1670) was an English royalist churchman, Dean of Bristol and Bishop of St Asaph.
He was educated at Trinity College, Oxford, where he matriculated on 15 October 1619, aged 16.
Glemham became rector of Symondsbury, Dorset, in 1631, leaving in 1645 when his brother Thomas was a prominent royalist figure.
In 1667 he was made Bishop of St Asaph, and became also rector of Llandrinio.
He died at Glemham Hall.