Kupa e Shqiperise 2019-20
| Match Schedule for Kukësi |  |
| MD | Date | Time | Home Team | Away Team | Result | ||||||
| 2 | 18.09.2019 | 18:00 h | Shkumbini |  | - |  | Kukësi | 1 | - | 3 |  |
| 3 | 02.10.2019 | 16:00 h | Kukësi | | - | | Shkumbini | 6 | - | 0 | |
| 4 | 29.01.2020 | 16:00 h | Lushnja |  | - | | Kukësi | 0 | - | 1 | |
| 5 | 12.02.2020 | 15:00 h | Kukësi | | - | | Lushnja | 3 | - | 0 | |
| 6 | 11.06.2020 | 19:00 h | Apolonia |  | - | | Kukësi | 1 | - | 2 | |
| 7 | 24.06.2020 | 18:30 h | Kukësi | | - | | Apolonia | 3 | - | 1 | |
| 8 | 01.07.2020 | 15:00 h | Kukësi | | - |  | Teuta | 0 | - | 0 |  |
| 9 | 15.07.2020 | 15:00 h | Teuta | | - | | Kukësi | 2 | - | 1 |  |