The defending champions were Linfield, who defeated Ballymena United 3–1 in the 1977–78 final.

Cliftonville went on to win the cup for the 8th time, defeating Portadown 3–2 in the final.

[2] This was Cliftonville's last Irish Cup success until the club won the Irish Cup for the first time in 45 years in 2024, though they had reached the final five times since this win; in 1997, 1999, 2009, 2013 and 2018.

1This tie required a replay, after the first game ended as a 0–0 draw.

[2] 2This tie required a replay, after the first game ended as a 2–2 draw.