| 1. Round | 13/09/1978 | Grasshopper Club Zürich | - | Valletta FC | 8:0 | ||||
| 1. Round | 27/09/1978 | Valletta FC | - | Grasshopper Club Zürich | 3:5 | ||||
| Round of 16 | 18/10/1978 | Real Madrid | - | Grasshopper Club Zürich | 3:1 | ||||
| Round of 16 | 01/11/1978 | Grasshopper Club Zürich | - | Real Madrid | 2:0 | ||||
| Quarter-finals | 07/03/1979 | Nottingham Forest | - | Grasshopper Club Zürich | 4:1 | ||||
| Quarter-finals | 21/03/1979 | Grasshopper Club Zürich | - | Nottingham Forest | 1:1 |  |
Switzerland