Principally two main bodies conduct the Affairs of the Academy: The Council, which is the governing body, and the General meeting of Fellows. The Council comprises the principal officers of the Academy namely; the President, two Vice Presidents who are respectively the Chairpersons of the Science and Arts Sections, the Honorary Secretary and the Honorary Treasurer together with six other persons elected by the General Meeting of Fellows from among the Fellows of the Academy. The Council meets at least twice a year.

The day-to-day administration of the Academy's Affairs is handled by a secretariat of full-time staff. These comprise an Administrative Secretary, a Deputy Administrative Secretary, a Senior Assistant Administrative Secretary, a Publications/Fundraising Officer as well as Secretarial and Clerical Staff who work under the general direction of the Honorary Secretary.

The more specialized work of the Academy is done by a number of committees appointed by the council. Presently there are nine principal committees namely: -

• Prizes and Awards Committee
• Publications Committee
• Programmes and Anniversary Celebrations Committee
• Budget and Finance Committee
• International Council for Sciences Committee
• Education Committee
• Resource Development Committee
• Special Projects Committee
• Christian Baeta Memorial Fund