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.
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.
If extra time was drawn, there was a replay at the ground of the team who were away for the first game.
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).