First, to decrease an amount of emitted nitrogen oxides to zero as much as possible and also decrease an amount of emitted carbon monoxide to a permissible level. Second, to save energy on combustion at a low air ratio close to 1.0. Third, to attain a stable air ratio control in a low air ratio combustion region.Included are a combustion step in which hydrocarbon-containing fuel is burned by the burner to generate gas free of hydrocarbons but containing oxygen, nitrogen oxides and carbon monoxide, an endothermic step in which endothermic device is used to absorb heat from gas generated in the combustion step, a hazardous-substance decreasing step in which the gas is brought into contact with an oxidation catalyst after the endothermic step to oxidize carbon monoxide contained in the gas by oxygen and reduce nitrogen oxides by carbon monoxide, and a concentration ratio adjusting step in which a concentration ratio of oxygen, nitrogen oxides and carbon monoxide in gas on the primary side of the oxidation catalyst is adjusted to a predetermined concentration ratio on the basis of concentration ratio characteristics of the burner and the endothermic device by using the air-ratio adjusting device of the burner.