Battle of Malplaquet
Smyth was the eldest son of Charles Smyth, MP for Limerick City, and Elizabeth Prendergast. His paternal grandparents were Thomas Smyth, Bishop of Limerick, and Dorothea Burgh (daughter of Ulysses Burgh), and his paternal uncles included the lawyer George Smyth and Arthur Smyth, Archbishop of Dublin. His maternal grandparents were Sir Thomas Prendergast, 1st Baronet, who was killed in action at the Battle of Malplaquet in 1709, and Penelope Cadogan, sister of William Cadogan, 1st Earl Cadogan.