| Year: | 1978–79 |
| Country: | Cyprus |
| Num Teams: | 40 |
| Dates: | 10 January 1979 – 24 June 1979 |
| Winners: | APOEL (11th title) |
| Next Season: | 1979–80 |
The 1978–79 Cypriot Cup was the 37th edition of the Cypriot Cup. A total of 40 clubs entered the competition. It began on 10 January 1979 with the preliminary round and concluded on 24 June 1979 with the final which was held at Makario Stadium. APOEL won their 11th Cypriot Cup trophy after beating AEL Limassol 1–0 in the final.
In the 1978–79 Cypriot Cup, participated all the teams of the Cypriot First Division, the Cypriot Second Division and the Cypriot Third Division.
The competition consisted of six knock-out rounds. In all rounds each tie was played as a single leg and was held at the home ground of one of the two teams, according to the draw results. Each tie winner was qualifying to the next round. If a match was drawn, extra time was following. If extra time was drawn, there was a replay at the ground of the team who were away for the first game. If the rematch was also drawn, then extra time was following and if the match remained drawn after extra time the winner was decided by penalty shoot-out.
The cup winner secured a place in the 1979–80 European Cup Winners' Cup.
In the first preliminary draw, participated all the 10 teams of the Cypriot Third Division and 6 of the 14 teams of the Cypriot Second Division (last six of the league table of each group at the day of the draw).
| width=30% align="right" | Team 1 | width=22% align="center" | Result | width=30% align="left" | Team 2 |
|---|---|---|---|---|---|
| (C) AEK Ammochostos | 1 - 2 | Olimpiada Neapolis (C) | |||
| (B) ASIL Lysi | 4 - 0 | ENAD Ayiou Dometiou (C) | |||
| (C) Doxa Katokopias | 1 - 3 | Anagennisi Deryneia (C) | |||
| (B) Iraklis Gerolakkou | 1 - 5 | AEM Morphou (B) | |||
| (C) Enosis Neon THOI Lakatamia | 2 - 0 | Achilleas Kaimakli (C) | |||
| (C) AEK Kythreas | 3 - 1 | Faros Acropoleos (C) | |||
| (C) Orfeas Nicosia | 3 - 0 | PAEEK (B) | |||
| (B) Parthenon Zodeia | 2 - 1 | Ethnikos Assia (B) | |||
16 clubs from the Cypriot First Division and the rest clubs from the Cypriot Second Division met the winners of the preliminary round ties:
| width=30% align="right" | Team 1 | width=22% align="center" | Result | width=30% align="left" | Team 2 |
|---|---|---|---|---|---|
| (A) AEL Limassol | 3 - 1 | Omonia Aradippou (A) | |||
| (B) AEM Morphou | 0 - 2 | Ethnikos Achna (B) | |||
| (A) Alki Larnaca | 3 - 2 | Ermis Aradippou (B) | |||
| (A) Anorthosis Famagusta | 10 - 1 | Enosis Neon THOI Lakatamia (C) | |||
| (A) Apollon Limassol | 2 - 0 | AEK Kythreas (C) | |||
| (A) APOP Paphos | 2 - 0 | Parthenon Zodeia (B) | |||
| (B) ASIL Lysi | 3 - 0 | Digenis Akritas Morphou (A) | |||
| 0 - 4 | Olympiakos Nicosia (A) | ||||
| (A) EPA Larnaca | 5 - 0 | Akritas Chlorakas (B) | |||
| 1 - 5 | Aris Limassol (A) | ||||
| (B) Neos Aionas Trikomou | 2 - 1 | Adonis Idaliou (B) | |||
| 0 - 6 | AC Omonia (A) | ||||
| 1 - 2 | Pezoporikos Larnaca (A) | ||||
| (A) Enosis Neon Paralimni | 10 - 0 | Olimpiada Neapolis (C) | |||
| (A) Nea Salamis Famagusta | 5 - 0 | Evagoras Paphos (A) | |||
| 1 - 2 | APOEL (A) | ||||
| width=30% align="right" | Team 1 | width=22% align="center" | Result | width=30% align="left" | Team 2 |
|---|---|---|---|---|---|
| 0 - 1 | Aris Limassol (A) | ||||
| (A) Anorthosis Famagusta | 2 - 1 | APOP Paphos (A) | |||
| (A) APOEL | 4 - 0 | Nea Salamis Famagusta (A) | |||
| (A) Apollon Limassol | 3 - 1 | ASIL Lysi (B) | |||
| 0 - 0, 1 - 4 | AC Omonia (A) | ||||
| 2 - 4 | Enosis Neon Paralimni (A) | ||||
| 1 - 2 | Olympiakos Nicosia (A) | ||||
| 0 - 2 | AEL Limassol (A) | ||||
| width=30% align="right" | Team 1 | width=22% align="center" | Result | width=30% align="left" | Team 2 |
|---|---|---|---|---|---|
| (A) AEL Limassol | 1 - 1, 3 - 0 | Apollon Limassol (A) | |||
| (A) Aris Limassol | 3 - 2 | AC Omonia (A) | |||
| (A) Olympiakos Nicosia | 0 - 3 | Anorthosis Famagusta (A) | |||
| (A) Enosis Neon Paralimni | 0 - 1 | APOEL (A) | |||
| width=30% align="right" | Team 1 | width=22% align="center" | Result | width=30% align="left" | Team 2 |
|---|---|---|---|---|---|
| (A) AEL Limassol | 2 - 0 | Aris Limassol (A) | |||
| (A) APOEL | 1 - 0 | Anorthosis Famagusta (A) | |||