An apparatus for filtering a suspension by at least one aggregate of membranes made of a high molecular weight compound porous hollow fibers to separate a filtrate from the suspended matter contained in the suspension, backwashing the aggregate of membranes with a backwashing gas to clean it and minimizing the amount of suspended matter entrained by the backwashing gas, and repeating the filtration and backwashing alternately, comprises a filtering vessel divided into a feed region and a filtrate region, the filtrate region being above the feed region, an inlet for the suspension at the feed region, an outlet for the filtrate at the filtrate region, an inlet for a backwashing gas in the filtrate region, an outlet for the backwashing gas in the feed region, a partition plate in the filtering vessel to support the aggregate of membrane filters and to divide the inteior of the filtering vessel into the filtrate region and the feed region, an outlet for a portion of the suspension in the feed region at a position lower than the outlet for the backwashing gas, a cylindrical protective case for housing the aggregate of membranes.