| 6. Round | 09/09/1959 | Nottingham Forest | - | Sheffield Wednesday | 2:1 | ||||
| 9. Round | 19/09/1959 | Everton FC | - | Sheffield Wednesday | 2:1 | ||||
| 10. Round | 26/09/1959 | Sheffield Wednesday | - | Luton Town | 2:0 | ||||
| 11. Round | 03/10/1959 | Bolton Wanderers | - | Sheffield Wednesday | 1:0 | ||||
| 32. Round | 05/03/1960 | Tottenham Hotspur | - | Sheffield Wednesday | 4:1 | ||||
| 34. Round | 19/03/1960 | Preston North End | - | Sheffield Wednesday | 3:4 |
Scotland