To improve unit requirement of an electrode in a melting furnace wherein a DC current is conducted to a waste incineration residue for melting by reducing the amount of consumption of the electrode.

An electrode 6 is constructed by connecting a graphite electrode 23 to tip end of a metal hollow electrode 22. A graphite part having large electric resistance is located only along the tip end of the electrode 6 and an upper part of the electrode 6 is formed with a metal having small electric resistance, so that heat production of the electrode 6 by conduction of the current is lowered, and oxidization consumption of the graphite electrode 23 due to its contact with oxygen in the furnace is reduced. Further, the metal hollow electrode 22 itself is prevented from being consumed, so that electrode consumption is sharply reduced. Provided that the metal hollow electrode 22 is cooled with water through a cooling pipe 24, the electrode consumption is further reduced.