PURPOSE: To achieve stable combustion in dust and sludge incineration by adjusting the amount of sludge supply, based on the supply speed of dusts and the conditions of combustion in the furnace.

CONSTITUTION: The sludge is dropped on the dusts in a chute hopper 1 from a sludge supply conveyor 9 through a sludge conveying piping 8 from a sludge conveyance pump 7. The temperature signal (a) for temperature detected by a furnace discharge temperature detector 5 is inputted to an automatic combustion controller 6. If a detected temperature exceeds a set value for lower limit, a signal (b) which stops the operation of a dust supply device 2 and a grate 3 is issued from the automatic combustion controller 6. A mixture incineration device 10 which is interlocked with the stop signal (b) also issues a signal (c) which stops a pump 7 and a conveyor 9. On the other hand a signal (d) for the speed of the dust supply device 2 and the grate 3 is inputted to the mixture incineration device 10. The signal (e) of a most appropriate amount of sludge supply which is calculated with the furnace discharge temperature signal (a) is issued to the pump 7 and the conveyor 9.