In a hydrogen generator comprising a reforming unit having a material supply unit and a water supply unit, and a burner for heating the reforming unit, having a fuel supply unit and an air supply unit, a control unit is arranged for controlling the amount of air to be supplied from the air supply unit to the burner, based on the temperature of the reforming unit and the amount of a raw material supplied to the reforming unit, in order to make the combustion state of the burner stable so as to improves the operation and convenience thereof.