1878–79 Heart of Midlothian F.C. season

Season 1878–79 was the fourth season in which Heart of Midlothian competed at a Scottish national level, entering the Scottish Cup for the fourth time.

Overview
Hearts reached the fourth round of the Scottish Cup, losing 2–1 to Helensburgh.

Hearts also reached the final of the Edinburgh FA Cup losing 2–0 to Hibs after a replay.