An election to Llanelli Borough Council was held in May 1979.[1] It was preceded by the 1976 election and followed by the 1983 election. On the same day there was a UK general election and were elections to the other district local authorities and community councils in Wales. The leader of the council was again Michael Willis Gimblett, who had held the role from the previous election.
Bowen had been elected as a Labour candidate in 1973 and 1976.