A humidifier is provided with a housing and a stacked unit inserted into the housing that is provided with water vapor-permeable membranes and frame parts, wherein the frame parts are stacked on each other and the water vapor-permeable membranes are arranged between the frame parts, respectively, so that the water vapor-permeable membranes are stacked on top of each other and are spaced apart from each other. The housing has supports that hold the stacked unit. The supports and the frame parts are connected to each other by a connection that is made of laterally projecting connecting tabs and a receiving groove extending in vertical direction, wherein the connecting tabs engage the receiving groove.