| 27. Ronde | 23.01.1960 | Chelsea FC | - | Leeds United | 1:3 | ||||
| 28. Ronde | 06.02.1960 | Leeds United | - | West Bromwich Albion | 1:4 | ||||
| 32. Ronde | 05.03.1960 | Leeds United | - | Blackpool FC | 2:4 | ||||
| 30. Ronde | 09.03.1960 | Leeds United | - | Birmingham City | 3:3 |  |
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| 34. Ronde | 19.03.1960 | Leeds United | - | Manchester City | 4:3 | |
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| 35. Ronde | 26.03.1960 | Arsenal FC | - | Leeds United | 1:1 | ||||
| 36. Ronde | 02.04.1960 | Leeds United | - | Wolverhampton Wanderers | 0:3 | ||||
| 37. Ronde | 09.04.1960 | Sheffield Wednesday | - | Leeds United | 1:0 | ||||
| 39. Ronde | 16.04.1960 | Leeds United | - | Bolton Wanderers | 1:0 | ||||
| 41. Ronde | 23.04.1960 | Everton FC | - | Leeds United | 1:0 | ||||
| 42. Ronde | 30.04.1960 | Leeds United | - | Nottingham Forest | 1:0 |
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