A humidifier includes a housing that accommodates bundles of a large number of water permeable hollow fiber membranes arranged along the longitudinal direction of the housing. Two different gasses having different moisture contents pass through outside and inside of the bundle of the hollow fiber membranes separately to exchange their moistures through the hollow fiber membranes resulting in the dry gas of lesser moisture content being humidified. A heating or temperature adjuster is provided to maintain the temperature of the exhaust gas introduced to the humidifier or the bundles of hollow fiber membranes substantially at a temperature of a fuel cell in operation.