To provide a method of discharging molten slag from a waste fusing furnace and a molten matter discharge structure which enable stable long-term continuous operation without slag and metal solidifying and blocking in a communication port, in a waste fusing furnace which is equipped with a front furnace connected with itself through the communication port.

The slag and metal are reserved once at the bottom of the fusion furnace 1, and to keep the reservoir 9 for fused slag, the position of installation of the discharge trough 12 of the front furnace 11 is set higher than the communication port 10 between the fusion furnace and the front furnace, and the communication port is always filled with metal, and also in the communication port, the slag and metal do not solidify to block it, and besides the temperature range where the corrosion of the refractory does not moves on is computed, and based on the computed value, the control temperature of the slag and metal in the discharge trough of the front furnace is set in advance, and in operation, the temperature of the slag and metal in the discharge trough of the front furnace is measured continuously, and the quantity of supplementary heating within the lower part of the fusion furnace is adjusted so that the measured value may come to the above control temperature.