| Exeter City FC v Notts County FC 06/02/1960 | View match | |
| Exeter City FC v Hartlepool United 20/02/1960 | View match | |
| Millwall FC v Exeter City FC 27/02/1960 | View match | |
| Exeter City FC v Southport 05/03/1960 | View match | |
| Gillingham FC v Exeter City FC 12/03/1960 | View match | |
| Exeter City FC v Barrow 19/03/1960 | View match | |
| Walsall FC v Exeter City FC 22/03/1960 | View match | |
| Aldershot F.C v Exeter City FC 26/03/1960 | View match | |
| Exeter City FC v Darlington FC 02/04/1960 | View match | |
| Gateshead v Exeter City FC 09/04/1960 | View match | |
| Crystal Palace FC v Exeter City FC 15/04/1960 | View match | |
| Exeter City FC v Rochdale FC 16/04/1960 | View match |