Season 1880–81 was the sixth season in which Heart of Midlothian competed at a Scottish national level, entering the Scottish Cup for the sixth time.
Hearts reached the fifth round of the Scottish Cup losing to Arthurlie.
[1] Hearts reached the third round of the Edinburgh FA Cup losing to city rival Hibs.
[2] On the way Hearts recorded their biggest known victory against Anchor winning 21–0.
[3]