A membrane filter apparatus includes a membrane unit 50 composed of an array of membrane elements 51 disposed within a treatment tank 31. A skirt element 71 is disposed at a bottom portion of the membrane unit and an aerator 61 is disposed under the skirt. A partition is also disposed at the bottom of the membrane unit forming compartments within the skirt element. The gas bubbles discharged from the aerator increase their rising force upon entry into gaps between the membranes. Because of the arrangement of the partition within the skirt element the flow rate of bubbles along the opposite side edge portions of the membrane unit can be increased having the advantage of cleaning the entire surface of each membrane, thereby preventing clogging by sludge, SS, colloid, etc. within the gaps between the membranes. Therefore, filtration can be maintained over a longer period of time and the power required for filtration can be reduced, as well as, the frequency of manual periodic cleaning, chemical cleaning, etc.