It is intended first to reduce the amount of nitrogen oxide emission next to zero and reduce the amount of carbon monoxide emission to tolerance levels; second to realize energy saving by combustion at a low air ratio close to 1.0; and third to stably carry out the control of air ratio within the combustion region at a low air ratio.; There is provided a boiler comprising a premix burner; a group of water pipes for heat exchanging with a gas produced by the premix burner to thereby restrict the temperature of the gas and suppress the concentration of nitrogen oxide to a given value or below; an oxidation catalyst for oxidizing by oxygen of carbon monoxide contained in the gas after pass through the group of water pipes and for reducing by carbon monoxide of nitrogen oxide contained therein; ; and air ratio regulation means for regulating of the air ratio of the premix burner, wherein the premix burner and the group of water pipes have characteristics such that when the air ratio is a preset air ratio, the concentration ratio of oxygen, nitrogen oxide and carbon monoxide in the gas on the primary side of the oxidation catalyst becomes a given concentration ratio, and wherein the oxidation catalyst has characteristics such that when the concentration ratio is a given concentration ratio, the concentration of nitrogen oxide on the secondary side of the oxidation catalyst is substantially zeroed while the concentration of carbon monoxide there is reduced substantially to zero or a given value or below, and wherein the given concentration ratio is held constant by regulation to preset air ratio by the air ratio regulation means.