A membrane filtration method and an apparatus for continuously monitoring the state of a membrane during the filtration, particularly for membrane fouling due to cake or gel layers of solutes developed on the surfaces of a filtered membrane, by estimating a membrane potential and a membrane solute rejection while making measurements of a set of physical properties of feed, variations of a streaming potential difference across pores of the membrane, variation in pressure differences between an upstream side and a downstream side of the membrane, and concentration differences between the feed and permeate filtered through the membrane.