Henry Conway may refer to:
- Sir Henry Conway, 1st Baronet (1630-1669), MP for Flintshire, of the Conway Baronets
- Henry Seymour Conway (1721-1795), British general and statesman
- Henry Wharton Conway (1793-1827), delegate from the Arkansas Territory to the United States House of Representatives
- Henry Conway (socialite), London-based socialite, club promoter and fashion journalist
- Henry Conway Belfield (1855–1923), British Resident in three Malay states and former Governor of Kenya.
- Lord Henry Seymour-Conway (1746–1830), former British and Irish MP.
- Harry Conway, Member of the Tasmanian House of Assembly, 1891–1893
- Conway (disambiguation)
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