| 1. Round | 22/08/1959 | Leeds United | - | Burnley FC | 2:3 | ||||
| 2. Round | 26/08/1959 | Leicester City | - | Leeds United | 3:2 | ||||
| 3. Round | 29/08/1959 | Luton Town | - | Leeds United | 0:1 | ||||
| 4. Round | 02/09/1959 | Leeds United | - | Leicester City | 1:1 | ||||
| 5. Round | 05/09/1959 | West Ham United | - | Leeds United | 1:2 | ||||
| 17. Round | 14/11/1959 | Wolverhampton Wanderers | - | Leeds United | 4:2 | ||||
| 19. Round | 28/11/1959 | Nottingham Forest | - | Leeds United | 4:1 | ||||
| 30. Round | 09/03/1960 | Leeds United | - | Birmingham City | 3:3 |
England