Akukweti was a tutor at the National Transport Institute of Tanzania from 1975 through 1977, after which he served as the institute's dean of students until 1981. He then worked as an administrative manager at the Tanzania Fisheries Research Institute until 1989, and co-ordinator and administrative manager at the Morogoro Oil Processing Company (MOPROCO) from 1989 until his election to parliament in 1990.