| 1. Round | 21/04/1979 | FC St. Gallen | - | Grasshopper Club Zürich | 0:0 | ||||
| 2. Round | 28/04/1979 | Grasshopper Club Zürich | - | FC Basel 1893 | 2:1 | ||||
| 3. Round | 08/05/1979 | FC Zürich | - | Grasshopper Club Zürich | 3:3 | ||||
| 4. Round | 12/05/1979 | Grasshopper Club Zürich | - | Servette FC | 0:1 | ||||
| 5. Round | 17/05/1979 | BSC Young Boys | - | Grasshopper Club Zürich | 1:0 | ||||
| 6. Round | 26/05/1979 | Grasshopper Club Zürich | - | FC St. Gallen | 0:1 | ||||
| 7. Round | 31/05/1979 | FC Basel 1893 | - | Grasshopper Club Zürich | 2:3 | ||||
| 8. Round | 13/06/1979 | Grasshopper Club Zürich | - | FC Zürich | 2:1 | ||||
| 9. Round | 16/06/1979 | Servette FC | - | Grasshopper Club Zürich | 3:1 | ||||
| 10. Round | 23/06/1979 | Grasshopper Club Zürich | - | BSC Young Boys | 0:0 |
Switzerland