| 1. Round | 14/09/1958 | RC Celta | - | Athletic Club | 0:3 | ||||
| 2. Round | 21/09/1958 | Espanyol Barcelona | - | RC Celta | 2:1 | ||||
| 3. Round | 28/09/1958 | RC Celta | - | Real Madrid | 2:4 | ||||
| 4. Round | 05/10/1958 | Sporting Gijón | - | RC Celta | 2:2 | ||||
| 5. Round | 12/10/1958 | RC Celta | - | UD Las Palmas | 0:0 | ||||
| 14. Round | 14/12/1958 | RC Celta | - | Granada CF | 3:0 | ||||
| 15. Round | 28/12/1958 | Sevilla FC | - | RC Celta | 2:0 | ||||
| 16. Round | 04/01/1959 | Athletic Club | - | RC Celta | 9:0 | ||||
| 17. Round | 11/01/1959 | RC Celta | - | Espanyol Barcelona | 1:2 | ||||
| 18. Round | 18/01/1959 | Real Madrid | - | RC Celta | 3:0 | ||||
| 22. Round | 15/02/1959 | RC Celta | - | Real Betis | 1:1 | ||||
| 28. Round | 05/04/1959 | RC Celta | - | Real Sociedad | 0:0 |
Spain