| Albion Rovers FC v Morton FC 14/11/1959 | View match | |
| Morton FC v Cowdenbeath FC 21/11/1959 | View match | |
| Morton FC v Queen Of The South FC 28/11/1959 | View match | |
| Morton FC v Gateshead 05/12/1959 | View match | |
| Forfar Athletic FC v Morton FC 12/12/1959 | View match | |
| St Johnstone FC v Morton FC 19/12/1959 | View match | |
| Morton FC v East Stirlingshire FC 26/12/1959 | View match | |
| Berwick Rangers FC v Morton FC 01/01/1960 | View match | |
| Morton FC v Brechin City FC 02/01/1960 | View match | |
| Queens Park FC v Morton FC 09/01/1960 | View match | |
| Morton FC v East Fife FC 16/01/1960 | View match | |
| Hamilton Academicals v Morton FC 23/01/1960 | View match |