Purpose: To provide a polymeric porous hollow fiber membrane which exhibits excellent fractionation performance and excellent permeability in treatment of a variety of aqueous fluids and also shows sufficient strength when incorporated into a module or used to treat a fluid, and which is excellent in aging stability in these performances and characteristics and is also excellent in membrane performance recoverability by washing, and which is especially suitable for treatment of a polyphenol-containing beverage and is expected to effectively harmonize the flavor of such a beverage. Solution: A polymeric porous hollow fiber membrane of the present invention is characterized in that (a) the hollow fiber membrane has skin layers on its inner and outer surfaces; (b) the diameters of the pores in the inner surface are smaller than the diameters of the pores in the outer surface; (c) the porosity tends to increase from the inner surface toward the outer surface, and then tends to decrease from at least one portion having a maximum porosity, of the wall section of the membrane, toward the outer surface; and (d) the hollow fiber membrane satisfies a relationship of 2 [%]≦DR≦20 [%], wherein the critical diameter of a fine particle to be removed, found by a fine particle-passing test, is φmax [μm]; the diameter of the pores in the inner surface is dIS [μm]; and the proportion of the pores with dIS exceeding φmax is DR [%] This polymeric porous hollow fiber membrane is also characterized in that the adsorption of polyphenol per a surface area of 1 m2 defined by the inner and outer surfaces of the membrane is from 50 to 500 mg.