| 1. Round | 19/08/1978 | Chelsea FC | - | Everton FC | 0:1 | ||||
| 2. Round | 22/08/1978 | Everton FC | - | Derby County | 2:1 | ||||
| 3. Round | 26/08/1978 | Everton FC | - | Arsenal FC | 1:0 | ||||
| 4. Round | 02/09/1978 | Manchester United | - | Everton FC | 1:1 | ||||
| 5. Round | 09/09/1978 | Everton FC | - | Middlesbrough FC | 2:0 | ||||
| 6. Round | 16/09/1978 | Aston Villa | - | Everton FC | 1:1 | ||||
| 7. Round | 23/09/1978 | Everton FC | - | Wolverhampton Wanderers | 2:0 | ||||
| 8. Round | 30/09/1978 | Bristol City | - | Everton FC | 2:2 | ||||
| 9. Round | 07/10/1978 | Everton FC | - | Southampton FC | 0:0 | ||||
| 10. Round | 14/10/1978 | Ipswich Town | - | Everton FC | 0:1 | ||||
| 11. Round | 21/10/1978 | Queens Park Rangers | - | Everton FC | 1:1 | ||||
| 12. Round | 28/10/1978 | Everton FC | - | Liverpool FC | 1:0 | ||||
| 13. Round | 03/11/1978 | Nottingham Forest | - | Everton FC | 0:0 | ||||
| 14. Round | 10/11/1978 | Everton FC | - | Chelsea FC | 3:2 | ||||
| 15. Round | 17/11/1978 | Arsenal FC | - | Everton FC | 2:2 | ||||
| 16. Round | 20/11/1978 | Everton FC | - | Manchester United | 3:0 | ||||
| 17. Round | 24/11/1978 | Norwich City | - | Everton FC | 0:1 | ||||
| 19. Round | 08/12/1978 | Birmingham City | - | Everton FC | 1:3 | ||||
| 20. Round | 15/12/1978 | Everton FC | - | Leeds United | 1:1 |
England