Francis Seymour-Conway, 1st Baron Conway of Ragley, 1st Baron Conway of Killultagh, MP, PC (Ire) (28 May 1679 – 3 February 1731/1732), was a British politician, born Francis Seymour.

From 1728 to 1732 Lord Conway was Governor of Carrickfergus and was sworn of the Irish Privy Council in 1728.

Lord Conway married firstly Lady Mary, daughter of Laurence Hyde, 1st Earl of Rochester, on 17 February 1703/1704.

They had four daughters: After Lady Mary's death in Northwicke on 25 January 1708/1709 he married secondly Jane Bowden, of Drogheda, in that same year, by whom he had two children: After Jane's death in Sandywell, Gloucestershire, on 13 February 1715/1716 he married thirdly Charlotte, daughter of John Shorter, of Bybrook, Kent, and wife, in July 1716.

Lord Conway died in February 1732 in Lisburn, aged 52, and was succeeded by his eldest son by his third wife, Francis Seymour-Conway, who was created Earl of Hertford in 1750 and Marquess of Hertford in 1793.