| 3. Round | 13/09/2020 | Olympiakos Nikosia | - | Doxa Katokopias | 1:2 |  |
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| 4. Round | 18/09/2020 | Ermis Aradippou | - | Olympiakos Nikosia | 0:1 | ||||
| 5. Round | 28/09/2020 | Olympiakos Nikosia | - | Paphos FC | 2:1 | ||||
| 6. Round | 03/10/2020 | Anorthosis Famagusta | - | Olympiakos Nikosia | 2:0 | ||||
| 7. Round | 19/10/2020 | Olympiakos Nikosia | - | Apollon Limassol | 0:1 | ||||
| 8. Round | 25/10/2020 | Ethnikos Achna | - | Olympiakos Nikosia | 1:3 | ||||
| 9. Round | 01/11/2020 | Olympiakos Nikosia | - | Omonia Nikosia | 1:0 | ||||
| 11. Round | 21/11/2020 | APOEL Nikosia | - | Olympiakos Nikosia | 0:1 | ||||
| 12. Round | 27/11/2020 | Olympiakos Nikosia | - | Karmiotissa Polemidion | 3:2 | |
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| 13. Round | 05/12/2020 | AEK Larnaca | - | Olympiakos Nikosia | 4:0 |  |
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| 16. Round | 24/12/2020 | Doxa Katokopias | - | Olympiakos Nikosia | 1:1 | ||||
| 14. Round | 28/12/2020 | AEL Limassol | - | Olympiakos Nikosia | 3:0 |  |
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| 19. Round | 11/01/2021 | Olympiakos Nikosia | - | Anorthosis Famagusta | 0:3 | ||||
| 20. Round | 17/01/2021 | Apollon Limassol | - | Olympiakos Nikosia | 2:1 | ||||
| 21. Round | 23/01/2021 | Olympiakos Nikosia | - | Ethnikos Achna | 1:2 |
Cyprus