The present invention has an object to provide a biomembrane filtration apparatus which can treat a nitrate nitrogen and nitrite nitrogen in an anaerobic state to stably remove them together with SS with efficiency and, simultaneously, can biologically remove the residual hydrogen donor as well remaining in the water to be treated in one and the same biomembrane filtration apparatus by a fixed bed biomembrane filtration method and a method therefore. As the means to achieve such an object, one embodiment of the present invention provides a biomembrane filtration apparatus having a packed layer packed with a particulate packing material to which microorganisms are to attach; an inlet for a liquid to be treated arranged above the packed layer to feed the liquid to be treated; and a gas feed opening arranged under the packed layer to feed a substantially oxygen-free gas or a gas containing trace amounts of oxygen.