1978–79 Albanian Cup (Albanian: Kupa e Shqipërisë) was the twenty-seventh season of Albania's annual cup competition. It began on August 1978 with the First Round and ended on 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.
The rounds were played in a two-legged format similar to those of European competitions. If the aggregated score was tied after both games, the team with the higher number of away goals advanced. If the number of away goals was equal in both games, the match was decided by extra time and a penalty shootout, if necessary.