To perform both the production of pure water due to electric deionization and the production of pure water due to ion exchange using an electric deionizing apparatus.

In a pure water making apparatus having the electric deionizing device constituted by providing a concentration chamber and cathode chamber 35, a desalting chamber 37 and an anode-side concentration chamber 40 by arranging ion exchange films 33', 34 and 33 between an anode 32 and a cathode 31 and filling the respective chambers with ion exchange resins, water to be treated is passed through the desalting chamber 37 in the state that the supply of a current is stopped or controlled so that current density becomes 1,000 mA/dm2 or below and subjected to ion exchange by the ion exchange resins 38 and 39 in the desalting chamber 37 to allow pure water to flow out of the desalting chamber 37.