An electrodeionization deionized water producing apparatus includes, between an anode chamber having an anode and a cathode chamber having a cathode, a desalination chamber in which a side near the anode is demarcated by an anion exchange membrane and a side near the cathode is demarcated by a cation exchange membrane and a concentrating chamber in which a side near the anode is demarcated by a cation exchange membrane and a side near the cathode is demarcated by an anion exchange membrane, and the anode side of the anion exchange membrane is filled with an anion exchanger. In the electrodeionization deionized water producing apparatus, water containing free carbon dioxide is supplied to the concentrating chamber and formation of scales in the concentrating chamber during a continuous operation of a long period is inhibited.