| 1. Round | 01/04/1978 | FC Sion | - | Grasshopper Club Zürich | 1:1 |  |
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| 2. Round | 08/04/1978 | Grasshopper Club Zürich | - | Lausanne Sports | 0:0 | ||||
| 3. Round | 15/04/1978 | FC Zürich | - | Grasshopper Club Zürich | 1:3 | |
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| 4. Round | 19/04/1978 | Grasshopper Club Zürich | - | Servette FC | 1:1 | ||||
| 5. Round | 22/04/1978 | FC Basel 1893 | - | Grasshopper Club Zürich | 2:0 | ||||
| 6. Round | 29/04/1978 | Grasshopper Club Zürich | - | FC Sion | 4:1 | ||||
| 7. Round | 06/05/1978 | Lausanne Sports | - | Grasshopper Club Zürich | 4:3 |
Switzerland