In an electrolyzer comprising an anode compartment provided with porous anodes, a cathode compartment, and a membrane providing a partition between the anode compartment and the cathode compartment, wherein a solution containing sulfide ions is introduced into the anode compartment, and an aqueous solution containing caustic soda is introduced into the cathode compartment, thereby producing a polysulfide containing polysulfide sulfur through electrolytic oxidation, wherein the anode compartment of the electrolyzer is cleaned with the use, of an aqueous solution containing at least either one of an inorganic acid, a chelating agent, and a scale-cleaning agent, thereby recovering performance of the electrolyzer. Further, when the contents of the anode compartment are replaced with an alkaline aqueous solution containing not more than 0.1 mass % of sulfide ions and not more than 0.1 mass % of carbonate ions upon stopping the electrolytic oxidation, thereby maintaining the performance of the electrolyzer.