An air filtering apparatus for filtering air includes a chamber having an air flow passage through which air flows, the chamber being connected through an air supply duct to a plurality of air blow-out ports opened to a large space, an air filtering portion that is disposed in the chamber and has a plurality of gas-liquid contact members for bringing air into contact with electrolytic water to filter the air, a water tank that is connected through a water feeding pump to a supply pipe for supplying the electrolytic water to each of the gas-liquid contact members of the air filtering portion, an electrolytic unit for generating the electrolytic water, and a mechanism for leading to the electrolytic unit a part of electrolytic water in the water tank which is sucked by the water feeding pump and supplied to the plurality of gas-liquid contact members through the supply pipe, electrolyzing the part of the electrolytic water in the electrolytic unit to further generate electrolytic water and returning the generated electrolytic water into the water tank.