| Morton FC v Dundee United FC 20/01/1968 | View match | |
| Airdrieonians (Old) v Morton FC 03/02/1968 | View match | |
| Morton FC v Stirling Albion FC 10/02/1968 | View match | |
| Aberdeen FC v Morton FC 12/02/1968 | View match | |
| Raith Rovers FC v Morton FC 02/03/1968 | View match | |
| St Johnstone FC v Morton FC 06/03/1968 | View match | |
| Clyde v Morton FC 16/03/1968 | View match | |
| Dunfermline Athletic v Morton FC 23/03/1968 | View match | |
| Morton FC v Hibernian FC 10/04/1968 | View match | |
| Morton FC v Falkirk FC 13/04/1968 | View match | |
| Morton FC v Rangers (Glasgow) FC 17/04/1968 | View match | |
| Celtic (Glasgow) FC v Morton FC 20/04/1968 | View match |