| 20. Round | 05/12/1959 | Leeds United | - | Fulham FC | 1:4 | ||||
| 21. Round | 12/12/1959 | Manchester City | - | Leeds United | 3:3 | ||||
| 22. Round | 19/12/1959 | Burnley FC | - | Leeds United | 0:1 | ||||
| 23. Round | 26/12/1959 | Leeds United | - | Tottenham Hotspur | 2:4 | ||||
| 39. Round | 16/04/1960 | Leeds United | - | Bolton Wanderers | 1:0 | ||||
| 38. Round | 18/04/1960 | Preston North End | - | Leeds United | 1:1 | ||||
| 40. Round | 19/04/1960 | Leeds United | - | Preston North End | 2:1 | ||||
| 41. Round | 23/04/1960 | Everton FC | - | Leeds United | 1:0 | ||||
| 33. Round | 27/04/1960 | Blackburn Rovers | - | Leeds United | 3:2 | ||||
| 42. Round | 30/04/1960 | Leeds United | - | Nottingham Forest | 1:0 |
England