| Morton FC v Heart Of Midlothian (Hearts) 18/11/1978 | View match | |
| Rangers (Glasgow) FC v Morton FC 25/11/1978 | View match | |
| Partick Thistle FC v Morton FC 09/12/1978 | View match | |
| Motherwell FC v Morton FC 16/12/1978 | View match | |
| Morton FC v Celtic (Glasgow) FC 23/12/1978 | View match | |
| Aberdeen FC v Morton FC 30/12/1978 | View match | |
| Morton FC v Rangers (Glasgow) FC 20/01/1979 | View match | |
| Morton FC v Partick Thistle FC 17/02/1979 | View match | |
| Hibernian FC v Morton FC 24/02/1979 | View match | |
| Dundee United FC v Morton FC 10/03/1979 | View match | |
| Morton FC v Motherwell FC 14/03/1979 | View match | |
| St Mirren FC v Morton FC 17/03/1979 | View match |