Rahim was born at village Mohonpur of Matlab Upazilla of Chandpur on 1 March 1921.
[1] Rahim went to America on a Fulbright scholarship in 1952 for higher education and a year later he again joined the History Department of Dhaka University.
[1] In 1953, he was admitted to the School of Oriental and African Studies (SOAS) under the University of London for Ph.D.
Rahim joined the history department of Dhaka University as a professor.
According to historian K. M. Mohsin, Rahim's Social and Cultural History of Bengal, published in Dukhand in 1963 and 1967, established him as a diligent researcher.