Season 1879–80 was the third in which Hibernian competed at a Scottish national level, entering the Scottish Cup for the third time.
Hibs reached the quarter-final of the Scottish Cup, losing 6–2 to Dumbarton.
Hibs defeated Edinburgh derby rivals Hearts in the third round, in a match played at Mayfield Park, in the Mayfield area of Edinburgh.
[1] All results are written with Hibs' score first.