| Dumbarton v Morton FC 13/02/1960 | View match | |
| Dundee United FC v Morton FC 20/02/1960 | View match | |
| Morton FC v Alloa Athletic FC 27/02/1960 | View match | |
| Morton FC v Stenhousemuir FC 05/03/1960 | View match | |
| Morton FC v Albion Rovers FC 19/03/1960 | View match | |
| Cowdenbeath FC v Morton FC 26/03/1960 | View match | |
| Queen Of The South FC v Morton FC 02/04/1960 | View match | |
| Morton FC v Montrose FC 16/04/1960 | View match | |
| Morton FC v Falkirk FC 20/04/1960 | View match | |
| Morton FC v Forfar Athletic FC 23/04/1960 | View match | |
| Morton FC v St Johnstone FC 30/04/1960 | View match | |
| Alloa Athletic FC v Morton FC 13/08/1960 | View match |