Hugh Alexander Law (1872 – 1 April 1943) was an Irish nationalist politician. He represented constituencies in County Donegal as a Member of Parliament (MP) in the United Kingdom House of Commons and later as a Teachta Dála (TD) in Dáil Éireann.
A barrister, Law was the grandson of Hugh Law (1818–1883), who had been Lord Chancellor of Ireland from 1881–1883. He was elected as an Irish Parliamentary Party MP for Donegal West at an unopposed by-election in April 1902, and was re-elected unopposed at successive general elections until he stood down at the 1918 general election, when the seat was won by Joseph Sweeney of Sinn Féin.
At the 1923 Irish general election, he was an unsuccessful Farmers' Party candidate for the 5th Dáil Éireann in the Donegal constituency. He stood again as a Cumann na nGaedheal candidate at the June 1927 general election and was elected to the 6th Dáil. Law was re-elected at the September 1927 general election, but lost his seat at the 1932 general election, and did not stand again.