NOVELTY - A cooling water circulation line (27) circulates cooling water to a pressure vessel (21) which stores a water electrolyzer (51). A control line (28) controls amount of circulation of cooling water to vessel, to a preset value based on the difference between internal pressure of the electrolyzer and pressure of water-filled portion of vessel, so that gap between vessel and electrolyzer is filled with water.    USE - For supplying hydrogen produced by electrolysis of water, to fuel cells.    ADVANTAGE - Enables exerting pressure on the electrolyzer, by filling the gap between the vessel and the electrolyzer with water, while ensuring required pressure-resistance of the vessel. Enables efficiently cooling the electrolyzer by circulating cooling water having preset flow rate. Prevents localized increase in the temperature of the polymeric electrolyte film, even when electrolysis is performed at a high pressure. Hence prevents damage to the electrolytic film. Prevents the failure of the O-ring provided in the electrolyzer.    DETAILED DESCRIPTION - The electrolyzer has a solid polymeric electrolyte film, an anode in which oxygen is generated, and a cathode in which hydrogen is generated. Hydrogen gas-water separator and oxygen gas-water separator are provided to separate water from hydrogen and oxygen gases, respectively. The control line operates based on the difference in pressure between pressure-vessel side of the cooling water circulation line, and hydrogen gas-water separator, or oxygen gas-water separator. A deionization unit (43) with a reverse osmosis film or ion-exchange film is provided in the cooling water circulation line. A pressing unit which exerts preset pressing force on the electrolyzer is provided in the apparatus. A cooling-water distributor is provided in the gap between the vessel and the electrolyzer.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of the hydrogen supply apparatus.    pressure vessel (21)    cooling water circulation line (27)    control line (28)    deionizing unit (43)    electrolyzer (51)