| Morton FC v Cowdenbeath FC 14/12/1963 | View match | |
| Raith Rovers FC v Morton FC 21/12/1963 | View match | |
| Morton FC v Stranraer 28/12/1963 | View match | |
| Ayr United FC v Morton FC 01/01/1964 | View match | |
| Morton FC v Stenhousemuir FC 02/01/1964 | View match | |
| Morton FC v Clyde 18/01/1964 | View match | |
| East Fife FC v Morton FC 01/02/1964 | View match | |
| Morton FC v Montrose FC 08/02/1964 | View match | |
| Berwick Rangers FC v Morton FC 15/02/1964 | View match | |
| Hamilton Academicals v Morton FC 22/02/1964 | View match | |
| Morton FC v Forfar Athletic FC 29/02/1964 | View match | |
| Stirling Albion FC v Morton FC 07/03/1964 | View match |