An apparatus for producing an alkali hydroxide, the apparatus having electrolytic cells each constructed by separating an anode chamber and a cathode chamber with an ion-exchange membrane, providing an anode in the anode chamber and providing a gas diffusion electrode in the cathode chamber, the apparatus being configured to conduct electrolysis while an aqueous alkali chloride solution is supplied to the anode chamber and while an oxygen-containing gas is supplied to the cathode chamber, the apparatus comprising: plural groups of the electrolytic cells connected in series in a current path, each group of the electrolytic cells comprising the electrolytic cells being layered, the electrolytic cells being connected in parallel or series in the current path, a flow passage configured such that cooling water being a coolant for cooling the electrolytic cells can pass therethrough being placed on a back-surface side of a wall facing the ion-exchange membrane across the cathode chamber of each electrolytic cell, a flow rate adjuster (V, V1 to V4) provided to each electrolytic cell or each group of electrolytic cells, the flow rate adjuster (V, V1 to V4) being able to individually adjust flow rates of the coolant passing through flow passages, a coolant supply passage for supplying the coolant to the flow passage, a heat exchanger for adjusting a temperature of the coolant to a set temperature, a pressure-adjusting valve and a pressure gauge placed at an upstream part of a part at which the coolant supply passage is branched corresponding to the group of the electrolytic cells in the coolant supply passage, the heat exchanger being placed between the pressure-adjusting valve and the pressure gauge in the coolant supply passage, a first controller configured such that an electrolytic current density provided based on a detected value of a current supplied to plural groups of the electrolytic cells is input thereto, the first controller being configured to provide a set pressure value of the coolant based on the electrolytic current density and a relation between the electrolytic current density and the set pressure value of the coolant, and to adjust a degree of opening of the pressure-adjusting valve based on a difference between the set pressure value and a pressure value measured by the pressure gauge, a thermometer placed downstream of the heat exchanger, a flow rate-adjusting valve, and a second controller configured to adjust a temperature of the coolant supplied to the electrolytic cells to a set temperature value by adjusting a supply amount of the coolant to the heat exchanger with the flow rate-adjusting valve based on a temperature value detected by the thermometer and the set temperature value. plural groups of the electrolytic cells connected in series in a current path, each group of the electrolytic cells comprising the electrolytic cells being layered, the electrolytic cells being connected in parallel or series in the current path, a flow passage configured such that cooling water being a coolant for cooling the electrolytic cells can pass therethrough being placed on a back-surface side of a wall facing the ion-exchange membrane across the cathode chamber of each electrolytic cell, a flow rate adjuster (V, V1 to V4) provided to each electrolytic cell or each group of electrolytic cells, the flow rate adjuster (V, V1 to V4) being able to individually adjust flow rates of the coolant passing through flow passages, a coolant supply passage for supplying the coolant to the flow passage, a heat exchanger for adjusting a temperature of the coolant to a set temperature, a pressure-adjusting valve and a pressure gauge placed at an upstream part of a part at which the coolant supply passage is branched corresponding to the group of the electrolytic cells in the coolant supply passage, the heat exchanger being placed between the pressure-adjusting valve and the pressure gauge in the coolant supply passage, a first controller configured such that an electrolytic current density provided based on a detected value of a current supplied to plural groups of the electrolytic cells is input thereto, the first controller being configured to provide a set pressure value of the coolant based on the electrolytic current density and a relation between the electrolytic current density and the set pressure value of the coolant, and to adjust a degree of opening of the pressure-adjusting valve based on a difference between the set pressure value and a pressure value measured by the pressure gauge, a thermometer placed downstream of the heat exchanger, a flow rate-adjusting valve, and a second controller configured to adjust a temperature of the coolant supplied to the electrolytic cells to a set temperature value by adjusting a supply amount of the coolant to the heat exchanger with the flow rate-adjusting valve based on a temperature value detected by the thermometer and the set temperature value.