To prevent soot, powder dust or the like which are generated at the time of incinerating combustible industrial wastes, from being discharged in the air, by collecting them in advance in an incinerator.

A method for incinerating combustible wastes comprises combusting the combustible wastes, directing the combustion gas resulted from the combustion of the combustible wastes into a horizontal exhaust flue 12, increasing weight of combustion dust in the combustion gas while decreasing pressure in the flue 12 by spraying water to the combustion gas which is moving in the flue 12, directing the combustion dust in the combustion gas, which has gained weight, from the flue 12 to a vertical exhaust flue 13 while performing further combustion by introducing additional combustion air to a combustion chamber with the decrease of pressure in the flue 12, collecting the combustion dust that has gained weight by directing it down to the flue 13 through wind selection, and directing vapor or the like other than the combustion dust up to the flue 13 for discharge in the air through a chimney.