To prevent a combustion gas containing hydrogen chloride and sulfide from directly hitting an outlet part of a rotary kiln furnace by forming a combustion air supply part for supplying combustion air into a stoker furnace on an air cooled wall of a gradated connection part of the rotary kiln furnace and the stoker furnace.

In an incinerator 1, a combustion air supply port part 6 is formed on an air-cooled wall 5 of a gradated connection part of a rotary kiln furnace 2 and a stoker furnace 3 to supply a part of combustion air A2 into the stoker furnace 3. During a series of incineration treatment period of matters to be burned drying and a partial combustion in the rotary kiln furnace 2 and gasification combustion and set combustion in the stoker furnace 3, a part of the combustion air A2 to be supplied into the stoker furnace 3 from the combustion air supply port part 6 formed on the air-cooled wall 5 of the gradated connection part coats the outlet part 2b of the rotary kiln furnace 2 with air, thereby keeping a combustion gas G containing hydrogen chloride and sulfide from directly hitting the outlet part 2b of the rotary kiln furnace 2.