Hydrogen ion-exchanged dealuminated mordenite having a reduced alumina content is advantageously prepared by filtering a crystallization slurry composed of a crystallization mother liquor and synthetic sodium type mordenite and obtained when the crystallization is completed, through a filter to form a wet cake layer of the sodium type mordenite; passing through the cake layer an aqueous solution of a mineral acid having a concentration of 0.1N to 5N; and then, washing the cake layer.