The Greek Cup 1977–78 was the 36th edition of The Greek Football Cup, or Greek Cup for short.
The competition culminated with the Greek Cup Final, held at Georgios Karaiskakis Stadium, Piraeus on 4 June 1978. The match was contested by AEK Athens and PAOK, with AEK Athens taking the title 2–0.
The 36th Greek Cup Final was played at the Georgios Karaiskakis Stadium, Piraeus.
- 90 minutes.
- 30 minutes of extra-time if necessary.
- Penalty shoot-out if scores still level.
- Two substitutes.