Alexander Hugh Baring, 4th Baron Ashburton, DL (4 May 1835 – 18 July 1889) was a British landowner and Conservative Party politician.
Baring was elected unopposed as a Member of Parliament (MP) for Thetford at a by-election in December 1857, filling the vacancy caused by his father's succession to the peerage. He was re-elected in 1859 and 1865, and held the seat until he succeeded to the peerage in 1868 on the death of his father.
On 16 June 1864, Baring was appointed to be a Deputy Lieutenant of the County of Norfolk. A member of the Baring family, he succeeded to the title of Baron Ashburton on 6 September 1868