| Bury FC v Exeter City FC 21/01/1978 | £4.00 | |
| Exeter City FC v Shrewsbury Town FC 28/01/1978 | View match | |
| Port Vale FC v Exeter City FC 08/02/1978 | View match | |
| Exeter City FC v Peterborough United FC 11/02/1978 | View match | |
| Portsmouth FC v Exeter City FC 28/02/1978 | View match | |
| Wrexham FC v Exeter City FC 04/03/1978 | View match | |
| Exeter City FC v Rotherham United FC 08/03/1978 | View match | |
| Exeter City FC v Lincoln City FC 11/03/1978 | View match | |
| Preston North End FC v Exeter City FC 18/03/1978 | £4.00 | |
| Exeter City FC v Swindon Town FC 22/03/1978 | View match | |
| Hereford United v Exeter City FC 25/03/1978 | View match | |
| Exeter City FC v Plymouth Argyle FC 28/03/1978 | View match |