| 1. Round | 26/09/1979 | Progrès Niedercorn | - | Grasshopper Club Zürich | 0:2 | ||||
| 1. Round | 03/10/1979 | Grasshopper Club Zürich | - | Progrès Niedercorn | 4:0 |  |
|||
| 2. Round | 24/10/1979 | Grasshopper Club Zürich | - | Ipswich Town | 0:0 | ||||
| 2. Round | 06/11/1979 | Ipswich Town | - | Grasshopper Club Zürich | 1:1 | ||||
| Round of 16 | 27/11/1979 | Grasshopper Club Zürich | - | VfB Stuttgart | 0:2 | ||||
| Round of 16 | 11/12/1979 | VfB Stuttgart | - | Grasshopper Club Zürich | 3:0 |
Switzerland