Akii-Bua started his athletic career as a hurdler on the short distance, but coached by British-born coach Malcolm Arnold, he was introduced to the 400 m hurdles. After finishing 4th in the 1970 Commonwealth Games and running the fastest season time in 1971, he was not a big favourite for the 1972 Summer Olympics in Munich, having limited competition experience. Nevertheless he won the final there, setting a World Record.

The government of Uganda did not appreciate the attention the athlete received, however, and placed him under house arrest. After missing the 1976 Olympics because of the African boycott, police officer Akii-Bua was even arrested . Eventually, he was freed by his shoe-manufacturer Puma and lived in Germany until the regime of Idi Amin ended in 1983.