A hydrogen generator and a method of operating the hydrogen generator. The hydrogen generator includes: a cylindrical reformer catalyst; and a cylindrical shift catalyst disposed inside of the reformer catalyst; a separation wall provided between the reformer catalyst and the shift catalyst; a cylinder that is disposed inside of the reformer catalyst, and comprises, on an outer surface thereof, a plurality of first nozzles to direct a plurality of flames to the reformer catalyst and a plurality of second nozzles to direct a plurality of flames to the shift catalyst; and a combustion fuel supply valve that selectively guides a combustion fuel to the first nozzles and or the second nozzles. The method includes heating the shift catalyst by supplying a combustion fuel to the second nozzles, making flames by igniting the combustion fuel that passes through the second nozzles, and directing the flames towards the shift catalyst, and stopping the heating of the shift catalyst by blocking the supply of the combustion fuel to the second nozzles when the temperature of the shift catalyst reaches the shift reaction temperature.