| 1. Round | 19/08/1978 | Bolton Wanderers | - | Bristol City | 1:2 | ||||
| 2. Round | 22/08/1978 | Bristol City | - | Norwich City | 1:1 | ||||
| 31. Round | 02/03/1979 | Bristol City | - | Manchester United | 1:2 | ||||
| 32. Round | 09/03/1979 | Arsenal FC | - | Bristol City | 2:0 | ||||
| 35. Round | 31/03/1979 | Bristol City | - | Birmingham City | 2:1 |  |
England