The method of an apparatus for incinerating and melting wastes along with incombustible materials in the wastes which comprise introducing wastes in a horizontal rotary furnace, incinerating the wastes at a temperature from 800.degree. C. to 1,200.degree. C., and melting the ashes of the wastes together with the remaining products which are vitrified at a temperature of more than 1,600.degree. C., by an oxygen type burner in which an oxygen-fuel mixture has an oxygen content of 50% in the mixture. The exhaust gas generated in the incineration and melting processes is introduced to a dust collector for cleaning the exhaust gas.