A simply configured cooling mechanism for an apparatus for producing hydrogen and oxygen is disclosed. The configuration makes it possible to freely select the type of heat exchanger, without any restrictions, in order to improve cooling efficiency. In particular, a heat exchanger for cooling deionized water in a deionized water tank, which contains an electrolytic cell, is installed outside the tank. An inlet to the heat exchanger is connected to a deionized water flow outlet from the tank that is below the level of the deionized water the tank by a pipe, and an outlet from the heat exchanger to tank is connected to a deionized water flow inlet that is positioned in the tank below the deionized water flow outlet.