James Stewart Barry Henderson (born 29 April 1936) is a former British Conservative Party politician who served in the House of Commons for two periods, February to October 1974 and 1979 to 1987, both for Scottish constituencies.
Henderson was educated at Stowe. He worked as a computer systems advisor and at the Scottish Conservative and Unionist Party Central Office.
Henderson contested Edinburgh East at the 1966 general election. He was first elected as the Member of Parliament (MP) for East Dunbartonshire at the February 1974 general election. Although a constituency of this name had existed before this election, because of large-scale boundary changes this was effectively a new constituency, and the sitting MP Hugh McCartney had moved to Central Dunbartonshire. However Henderson lost his seat at the October 1974 election, to Margaret Bain of the Scottish National Party, by only 22 votes.
At the 1979 general election, he was returned to Parliament as MP for East Fife. After boundary changes for the 1983 general election he was elected for North East Fife, which was largely the same constituency with only limited boundary changes. However he lost his seat at the 1987 general election to Menzies Campbell of the Liberal Democrats.