| 6. Round | 09/09/1978 | BSC Young Boys | - | Grasshopper Club Zürich | 2:0 | ||||
| 8. Round | 23/09/1978 | Neuchâtel Xamax FC | - | Grasshopper Club Zürich | 0:0 | ||||
| 10. Round | 14/10/1978 | Grasshopper Club Zürich | - | FC St. Gallen | 2:3 | ||||
| 11. Round | 21/10/1978 | FC Chiasso | - | Grasshopper Club Zürich | 1:1 | ||||
| 12. Round | 28/10/1978 | Grasshopper Club Zürich | - | FC Sion | 2:1 | ||||
| 13. Round | 05/11/1978 | FC Zürich | - | Grasshopper Club Zürich | 1:1 | ||||
| 14. Round | 19/11/1978 | Grasshopper Club Zürich | - | Lausanne Sports | 3:0 |  |
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| 15. Round | 26/11/1978 | FC Nordstern Basel | - | Grasshopper Club Zürich | 1:1 | |
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| 16. Round | 03/12/1978 | Grasshopper Club Zürich | - | BSC Young Boys | 2:2 | ||||
| 17. Round | 03/03/1979 | CS Chênois | - | Grasshopper Club Zürich | 0:0 | ||||
| 18. Round | 13/03/1979 | Grasshopper Club Zürich | - | Neuchâtel Xamax FC | 2:2 | ||||
| 19. Round | 17/03/1979 | Grasshopper Club Zürich | - | FC Basel 1893 | 2:1 | ||||
| 20. Round | 31/03/1979 | FC St. Gallen | - | Grasshopper Club Zürich | 1:3 | ||||
| 21. Round | 04/04/1979 | Servette FC | - | Grasshopper Club Zürich | 0:0 | ||||
| 22. Round | 07/04/1979 | Grasshopper Club Zürich | - | FC Chiasso | 4:0 |
Switzerland