| Morton FC v St Johnstone FC 31/12/1937 | View match | |
| Falkirk FC v Morton FC 01/01/1938 | View match | |
| Morton FC v Motherwell FC 03/01/1938 | View match | |
| Morton FC v Partick Thistle FC 08/01/1938 | View match | |
| Ayr United FC v Morton FC 15/01/1938 | View match | |
| Morton FC v Hibernian FC 29/01/1938 | View match | |
| St Mirren FC v Morton FC 05/02/1938 | View match | |
| Aberdeen FC v Morton FC 19/02/1938 | View match | |
| Arbroath FC v Morton FC 26/02/1938 | View match | |
| Clyde v Morton FC 16/03/1938 | View match | |
| Hamilton Academicals v Morton FC 19/03/1938 | View match | |
| Morton FC v Rangers (Glasgow) FC 26/03/1938 | View match |