The Greek Cup 1978–79 was the 37th edition of The Greek Football Cup, or Greek Cup for short.
Totally 58 teams participated, 18 from Alpha Ethniki and 40 from Beta Ethniki. It was held in 6 rounds, included final. That year was established for first time the two-legged tie on a home and away basis, for the quarter-finals and the semi-finals, according to the model of European cups.
Up to those matches, the most interesting round was Third. By 8 matches, only 2 were judged into 90 minutes. In matches between Aris and Panathinaikos and Olympiacos and PAOK, the home teams qualified in penalty shootout. With this rule, Aris had earlier eliminated Iraklis.
The final was contested by champion of that season, AEK Athens, and Panionios, that qualified in a Greek Cup Final after 12 years. Panionios made a surprise by eliminating both Aris, in quarter-finals, with a 5–1 victory - inversion in their home, after their defeat 5–2 in Aris' home, and Olympiacos, in semi-finals, with away goals rule. The surprise was completed in final, held at Georgios Karaiskakis Stadium, Piraeus on 9 June 1979, where Panionios took the title 3–1, winning at the same time their first title in their history.