| Bristol City FC v Swansea Town 05/03/1960 | £5.00 | |
| Swansea Town v Scunthorpe United FC 12/03/1960 | View match | |
| Middlesbrough FC v Swansea Town 19/03/1960 | View match | |
| Swansea Town v Cardiff City FC 26/03/1960 | View match | |
| Hull City FC v Swansea Town 02/04/1960 | View match | |
| Swansea Town v Sheffield United FC 09/04/1960 | View match | |
| Leyton Orient FC v Swansea Town 15/04/1960 | View match | |
| Plymouth Argyle FC v Swansea Town 16/04/1960 | View match | |
| Swansea Town v Leyton Orient FC 18/04/1960 | View match | |
| Swansea Town v Derby County FC 23/04/1960 | View match | |
| Swansea Town v Bristol City FC 26/04/1960 | View match | |
| Rotherham United FC v Swansea Town 30/04/1960 | View match |