To provide a combustion apparatus and a controlling method therefor which are capable of preventing the flame-out and backfire of the flame of a premix burner and the increase of the NOx concentration attributable to the change of the calorific value of the fuel, the amount of air supplied to the premix burner is so controlled as to achieve a low NOx within the range in which the premix burner effects a stable combustion in accordance with the calorie of the fuel supplied to the combustion apparatus, and a change of the output of the combustion apparatus attributable to this control of the amount of air is compensated by the control of the amount of the fuel supplied to the diffusion burner.