| Rangers (Glasgow) FC v Dundee 09/02/1960 | View match | |
| Dundee v St Mirren FC 27/02/1960 | View match | |
| Hibernian FC v Dundee 29/02/1960 | View match | |
| Arbroath FC v Dundee 05/03/1960 | View match | |
| Ayr United FC v Dundee 09/03/1960 | View match | |
| Dunfermline Athletic v Dundee 12/03/1960 | View match | |
| Dundee v Partick Thistle FC 19/03/1960 | View match | |
| Dundee v Hibernian FC 26/03/1960 | View match | |
| Airdrieonians (Old) v Dundee 02/04/1960 | View match | |
| Dundee v Celtic (Glasgow) FC 16/04/1960 | View match | |
| Dundee v Stirling Albion FC 23/04/1960 | View match | |
| Third Lanark v Dundee 30/04/1960 | View match |