PURPOSE: To prevent the generation of poisonous gas and improve incinerating efficiency so as not to produce remaining unburnt constituents, upon incineration of waste of polymeric substances such as waste plastics and the like.

CONSTITUTION: A fire grate 4 is formed of a plurality of air dispersing tubes below a primary combustion furnace 2 and a hollow conical guide body 5, whose lower end is opened, is put on the central upper surface of the fire grate 4 to constitute the guide body 5 so that a part of combustion air is sent out of the through holes 5b of the guide body 5. Thermal decomposition of waste plastics P, thrown into the furnace, is effected under partial combustion condition and generated combustible gas is guided into a secondary combustion furnace 12 through a ventilating port 7 and a duct 8 to effect complete combustion by an assistant combustion burner 14 in a combustion chamber 13. In this case, the molten substances of the waste plastics will never make one block at the central part of the fire grate 4 whereby the partial combustion can be maintained and the thermal decomposition can be promoted.