James Hay Erskine Wemyss (29 August 1829 – 29 March 1864) was a Scottish Member of Parliament, representing Fife from 1859 until his death.
He was the son of James Erskine Wemyss by his wife Emma, daughter of William Hay, 17th Earl of Erroll. In 1855 he married Millicent Anne Mary, daughter of the Hon. John Kennedy-Erskine and his wife Lady Augusta Fitzclarence. She was the granddaughter of Archibald Kennedy, 1st Marquess of Ailsa and of King William IV of the United Kingdom. Their children included Dora Mina, who married Lord Henry Grosvenor and was the mother of William Grosvenor, 3rd Duke of Westminster; Randolph Gordon, who inherited the Wemyss estates and is the ancestor of the present Chief of Clan Wemyss; and Rosslyn Wemyss, 1st Baron Wester Wemyss, who served as First Sea Lord during the First World War.