Smith was the son of a descendant of English army officers and merchants, and his mother was a black nurse who died in childbirth.
Born in Kingston, Jamaica, Smith attended Jamaica College one of the island's leading secondary schools where he developed a passion for poetry. In the early 1940s he left the island on scholarship to study English Literature at McGill University in Canada. Joining the Canadian army during the war, he served briefly on the frontline in Europe.
After being demobilized he enrolled at University College, London, which awarded him the Ph.D in social anthropology. He subsequently carried out extensive field research in Northern Nigeria, Jamaica, Grenada, and Carriacou.
Smith served as Franklin M. Crosby Professor Emeritus of the Human Environment at Yale University. He also served as Senior Research Fellow at the Research Institute for the Study of Man, and the Institute of Social and Economic Research, University of the West Indies (Jamaica); Professor of Anthropology at the University of California, Los Angeles; and as Professor and Head of the Department of Anthropology, University College, London, where he was one of the first professors of colour in Anthropology.