The 1979–80 Cypriot Cup was the 38th edition of the Cypriot Cup. A total of 41 clubs entered the competition. It began on 10 November 1979 with the preliminary round and concluded on 29 June 1980 with the replay final which was held at Makario Stadium. Omonia won their 4th Cypriot Cup trophy after beating Alki Larnaca 3–1 in the final.

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In the 1979–80 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 1980–81 European Cup Winners' Cup.

In the first preliminary draw, participated all the 12 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).

15 clubs from the Cypriot First Division and the rest clubs from the Cypriot Second Division met the winners of the preliminary round ties:

• "1979/80 Cyprus Cup". Rec.Sport.Soccer Statistics Foundation. 2017-08-08. Retrieved 2017-08-08.

• Cypriot Cup
• 1979–80 Cypriot First Division