PURPOSE: To burn not-yet-burnt combustible materials included in burnt ashes perfectly by a method wherein high pressure gas is injected from below the fire grid of the furnace to make the burnt ashes floated in high temperature gas within the combustion chamber.

CONSTITUTION: In a garbage incinerator 1 of stepped type, wastes such as garbage are thrown into the furnace from a hopper 2 and burnt successively passing through a drying stoker 3, a burning stoker 4 and a post-burning stoker 5 through supply of combustion air. High pressure gas 7 is injected from a final stage 6 of the post- burning stoker 5 to contact not-yet-burnt combustible materials in burnt ashes with high temperature gas at a high temperature gas region 9 within a combustion chamber 8 and then make them perfectly burnt in the floating state. Burnt ashes are collected together with high temperature gas via a smoke path 10 by a cyclon or others. From an outlet 11 are exhausted only incombustible clinker and metals.