He was born to Ali bin Abdallah Kighoma Malima and Habiba bint Suleiman wa Bura.

Malima cut short his studies in 1957 to join TANU and struggle for independence under the leadership of Julius Nyerere.

In June 1961 he attended a short course at Kivukoni Ideological College, Dar es Salaam before leaving for United States in 1962 for further studies at Dartmouth College, Hanover, New Hampshire where he obtained a BA in economics in 1965.

Few months later they got married and moved to New Haven were Kighoma Malima went to pursue his MA Economics at Yale University and graduated in 1966.

Soon after he began to work on his Ph.D. (International Trade and Economic Development) from Princeton University which he successfully defended in 1971.