| Club: | Hibernian |
| Season: | 1878–79 |
| League: | None |
| Cup1: | Scottish Cup |
| Cup1 Result: | R5 |
| Prevseason: | 1877–78 |
| Nextseason: | 1879–80 |
Season 1878–79 was the second in which Hibernian competed at a Scottish national level, entering the Scottish Cup for the second time.
Hibs reached the fifth round of the Scottish Cup, losing 2–1 to Helensburgh.
The club began using a ground in the Powderhall area of Edinburgh during this season.[1]
All results are written with Hibs' score first.
| Date | Round | Opponent | Venue | Result | Attendance | Scorers | |
|---|---|---|---|---|---|---|---|
| 28 September 1878 | R1 | Dunfermline | H | 5–2 | |||
| 19 October 1878 | R2 | 3rd Edinburgh RV | H | 3–0 | Quinn, Donnelly, Heron | ||
| 16 November 1878 | R3 | Edinburgh University | A | 5–2 | Flynn (2), Rourke (3) | ||
| 7 December 1878 | R4 | Rob Roy | H | 9–0 | |||
| 8 March 1879 | R5 | Helensburgh | A | 1–2 | Donnelly |