| Arsenal FC v Everton FC 20/02/1960 | £6.50 | |
| Arsenal FC v Everton FC 20/02/1960 | £7.50 | |
| Everton FC v Preston North End FC 27/02/1960 | View match | |
| West Ham United FC v Everton FC 05/03/1960 | View match | |
| Everton FC v Chelsea FC 12/03/1960 | View match | |
| West Bromwich Albion FC v Everton FC 19/03/1960 | View match | |
| Everton FC v Newcastle United FC 25/03/1960 | View match | |
| Birmingham City FC v Everton FC 02/04/1960 | View match | |
| Everton FC v Tottenham Hotspur FC 09/04/1960 | View match | |
| Everton FC v Blackpool FC 15/04/1960 | View match | |
| Leicester City FC v Everton FC 16/04/1960 | View match | |
| Blackpool FC v Everton FC 18/04/1960 | View match |