John Alcindor (8 or 9 July 1873–25 October 1924) was a physician from Trinidad who settled in London. He is known for his role in the African Progress Union.
He was educated at Saint Mary's College and then went as a medical student to Edinburgh University on a scholarship. He graduated there with a medical degree in 1899. He then worked in London hospitals, going into practice on his own around 1907. At this period he played cricket, as a wicket keeper for London teams.
Refused a place in the Royal Army Medical Corps, Alcindor was awarded a Red Cross medal for his work with the wounded at London rail stations during World War I.
Alcindor served as senior district medical officer in Paddington from 1921 to his death.
Alcindor associated in the late 1890s with the group around Henry Sylvester-Williams and his African Association. They were behind the First Pan-African Conference in 1900, which he attended in London, as a delegate from the Afro-West Indian Society.
Alcindor became the second president of the African Progress Union in 1921, succeeding John Archer.
Alcindor presided on the first day of the 2nd Pan-African Congress in 1921, with Rev. W. H. Jernagin. He spoke at the 3rd Pan-African Congress in 1923.
In July 2014 a blue plaque in his honour was unveiled at the site of Alcindor's surgery, which is now the Medical Centre in Harrow Road, Paddington.