PURPOSE: To execute stable melting by arranging slag supplying device for supplementing the slag so as to suitably maintain depth of the molten slag.

CONSTITUTION: Electro slag remelting operation is started under condition of beforehand charging suitable quantity of the slag in a hollow part of inner part of a cooling mold 4 and a hollow steel ingot 5. As the remelting progresses, the slag is consumed and it becomes condition of lower than the suitable depth of the molten slag, to be not able to obtain the stable melting condition. Therefore, in order to supplement the consumed slag during remelting, the same quantity of the slag as the consumed slag quantity is dropped and added into the hollow part of the inner part of the hollow steel ingot 5 from the slag supplying device 26 arranged above the hollow steel ingot 5 and a slag supplying hole 22. As a table 30 is rotated with a table rotating device 25 during melting, the slag is uniformly supplied in the hollow part of the ingot. By this method, the depth of the molten slag is maintained in the suitable range for melting condition and the stable melting is executed.