| Morton FC v Third Lanark 20/12/1919 | View match | |
| Heart Of Midlothian (Hearts) v Morton FC 27/12/1919 | View match | |
| Morton FC v Clyde 01/01/1920 | View match | |
| Morton FC v Partick Thistle FC 03/01/1920 | View match | |
| Morton FC v St Mirren FC 05/01/1920 | View match | |
| Celtic (Glasgow) FC v Morton FC 10/01/1920 | View match | |
| Morton FC v Albion Rovers FC 17/01/1920 | View match | |
| Hamilton Academicals v Morton FC 31/01/1920 | View match | |
| Morton FC v Rangers (Glasgow) FC 14/02/1920 | View match | |
| Morton FC v Ayr United FC 13/03/1920 | View match | |
| Airdrieonians (Old) v Morton FC 20/03/1920 | View match | |
| Motherwell FC v Morton FC 03/04/1920 | View match |