It began on 8 May 1976 with the preliminary round and concluded on 27 June 1976 with the final which was held at Tsirio Stadium.
APOEL won their 9th Cypriot Cup trophy after beating Alki Larnaca 6–0 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.
Achilleas Kaimakli, a team of 1975–76 Cypriot Third Division didn't want to participate in the 1975–76 Cyprus Cup, so only 7 of the 8 teams of the 1975–76 Cypriot Third Division participated.