It began on 13 October 1935 with the quarterfinals and concluded on 3 November 1935 with the final which was held at GSP Stadium.
Enosis Neon Trust won their 2nd Cypriot Cup trophy after beating Lefkoşa Türk Spor Kulübü 1–0 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 a match was drawn, extra time was following.
If extra time was drawn, there was a replay match.