| Club: | Heart of Midlothian |
| Season: | 1878–79 |
| Cup1 Result: | 4th Round |
| Prevseason: | 1877–78 |
| Nextseason: | 1879–80 |
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.
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.
See main article: 1878–79 Scottish Cup.
See main article: East of Scotland Shield.