 His father became 9th Baronet of Dalvey in 1854 on the death of his brother, Sir Alexander Grant, 8th Baronet.When his father died in 1856 Alexander became the 10th baronet.In 1859 he went to Madras with Sir Charles Trevelyan, and was appointed inspector of schools; the next year he moved to Bombay, to fill the post of Professor of History and Political Economy in the Elphinstone College.