Abstract: An electrolytic cell and method of electrolysis for producing hydrogen peroxide at a moderate current density while preventing metal deposition on the cathode surface. A feed water from which multivalent metal ions have been removed and in which a salt of a univalent metal, e.g., sodium sulfate, has been dissolved in a given concentration is prepared with an apparatus for removing multivalent metal ions and dissolving a salt in low concentration. The feed water is supplied to an electrolytic cell. Even when electrolysis is continued, almost no deposition of a hydroxide or carbonate occurs on the cathode because multivalent metal ions are not present in the electrolytic solution. Due to the dissolved salt, a sufficient current density is secured to prevent an excessive load from being imposed on the electrodes, etc. Thus, stable production of hydrogen peroxide is possible over a long period of time.