The Museum of Archaeology is a teaching museum located in the Department of Archaeology and Heritage Studies at the University of Ghana, Legon. The museum has its beginnings at Achimota College, an experimental educational institution that was opened in 1924 at Achimota, near Accra. Prof Charles Thurstan Shaw, a British archaeologist and the first trained archaeologist to work in Ghana, began the museum collections by gathering artifacts unearthed during the construction of Achimota College. In 1927, Prof Shaw opened a small museum at Achimota College to house the specimens, one of the first of such institutions in West Africa. Word about this spread, and missionaries, colonists, businessmen, academics and adventurers began sending artifacts to Shaw from across the continent. The museum displays were intended to be self-explanatory and demonstrative exhibits although they were not often used directly in teaching.

From 1937–1945, Shaw initiated a symbiotic relationship between archaeology and museums. He carried out the first scientific archaeological excavations and also collected diverse ethnographic materials from different parts of the country. All of these archaeological and ethnographic materials became part of the collections with which the Achimota College Museum of Anthropology was established with Thurstan Shaw as the curator. In 1951, the Achimota Museum was dissolved to give way for the establishment of the Department of Archaeology at the University College of the Gold Coast (present-day University of Ghana, Legon) in the same year. Then in 1952, the Achimota Museum collections in their entirety were transferred to the Department of Archaeology, Legon for safekeeping. This transfer served as the nucleus around which the Museum of Archaeology grew. This was also occurred in the period during which the Ghana National Museum was being completed based partly on the ideas proposed by Julian Huxley, Max Gluckman, and Governor Alan Burns and later refined by the British Museum’s H. J. Braunholtz.