To provide an incinerator, capable of protecting a member, on which oxidation resistant treatment is applied, in cases when combustion condition is fluctuated suddenly, much amount of combustible waste is supplied and substances, having high heating value, are included.

An auxiliary combustion space, an exhaust gas discharging means 3, a dust removing means 7 for removing powder dust included in the exhaust gas and a combustion oxygen supplying means 4a, supplying combustion oxygen into the incinerator 1, are provided. An oxygen supplying amount control means 9, controlling the amount of oxygen supplied from the combustion oxygen supplying means 4a so as to maintain the combustion heat of the auxiliary combustion space within a predetermined range by controlling combustion in the incinerator 1 by the detecting temperature of a temperature detecting means 8 provided in the dust removing means 7, is provided. A cooling oxygen supplying means 4b is provided between the auxiliary combustion space and the dust removing means 7. The oxygen supplying amount control means 9 controls the amount of oxygen supplied from the combustion oxygen supplying means 4a and the cooling oxygen supplying means 4b by the detecting temperature of the temperature detecting means 8. The auxiliary combustion space is an auxiliary incinerator 2 or the upper space of the incinerator 1.