A combustion method and apparatus in which combustible matter, e.g., waste matter, coal, etc., is gasified to produce a combustible gas containing a sufficiently large amount of combustible component to melt ash by its own heat. A fluidized-bed furnace has an approximately circular horizontal cross-sectional configuration. A moving bed, in which a fluidized medium settles and diffuses, is formed in the central portion of the furnace, and a fluidized bed, in which the fluidized medium is actively fluidized, is formed in the peripheral portion in the furnace. The fluidized medium is turned over to the upper part of the moving bed from the upper part of the fluidized bed, thus circulating through the two beds. Combustible matter is cast into the upper part of the moving bed and gasified to form a combustible gas while circulating, together with the fluidized medium. The amount of oxygen supplied to the fluidized-bed furnace is set so as to be not higher than 30% of the theoretical amount of oxygen required for combustion. The temperature of the fluidized bed is maintained at 450.degree. C. to 650.degree. C. so that the combustible gas produced contains a large amount of combustible component. The combustible gas and fine particles produced in the fluidized-bed furnace are supplied to a melt combustion furnace where they are burned at high temperature, and the resulting ash is melted.