1978–79 Albanian Cup (Albanian: Kupa e Shqipërisë) was the twenty-seventh season of Albania's annual cup competition. It began in August 1978 with the First Round and ended in May 1979 with the Final matches. The winners of the competition qualified for the 1979-80 first round of the UEFA Cup. Dinamo Tirana were the defending champions, having won their ninth Albanian Cup last season. The cup was won by KS Vllaznia.