To provide an incineration method and apparatus for waste wherein production of harmful matter such as dioxins is greatly and sharply suppressed without requiring conspicuous high temperature calcination and addition of a neutralizing material.

When combustible waste containing or producing harmful matter is converted to an emulsion fuel or an emulsion fuel is auxiliarily added and is incinerated, string electric field enough to ionize and disperse the emulsion fuel is added to the emulsion fuel, and the combustible waste is preheated with incineration heat of itself and completely combust while bringing waste smoke by incineration into contact with a heat storage structure and catalytic metal.