To keep temperature in a melting chamber unchanged with the low operation cost.

Ash entrained with thermal decomposition gas is melted to produce slag by throwing waste into a fluidized bed of a gasifying furnace 1 in the state of insufficient oxygen and introducing the thermal decomposition gas into a melting chamber 22 for combustion at high temperature. After the slag is captured from combustion waste gas, and when the slag is completely combusted in a secondary combustion chamber 25 and is exhausted, uncombustible matter and uncombusted carbon fraction are separated from a bed member pulled from the gasifying furnace 1 with a vibration shieving apparatus 8, and the bed member after the separation is circulated to the gasifying furnace 1, and the uncombusted carbon fraction is thrown into the melting chamber 22 from an uncombusted carbon fraction supply line 27 for combustion.