| Morton FC v Motherwell FC 03/09/1904 | View match | |
| Morton FC v Kilmarnock FC 10/09/1904 | View match | |
| Partick Thistle FC v Morton FC 17/09/1904 | View match | |
| St Mirren FC v Morton FC 24/09/1904 | View match | |
| Morton FC v Third Lanark 01/10/1904 | View match | |
| Motherwell FC v Morton FC 08/10/1904 | View match | |
| Dundee v Morton FC 15/10/1904 | View match | |
| Morton FC v Partick Thistle FC 29/10/1904 | View match | |
| Port Glasgow Athletic v Morton FC 05/11/1904 | View match | |
| Morton FC v Airdrieonians (Old) 12/11/1904 | View match | |
| Morton FC v Hibernian FC 19/11/1904 | View match | |
| Queens Park FC v Morton FC 03/12/1904 | View match |