A polymeric porous hollow fiber membrane comprising a hydrophobic polymer which is a polysulfone-based polymer and a hydrophilic polymer which is polyvinyl pyrrolidone, characterized in that (a) the hollow fiber membrane has skin layers on its inner and outer surfaces; wherein the portion on the rear sides of the skin layers is a sponge-like support layer having pores with larger diameters and a higher porosity than those of the skin layers; (b) the diameters of pores in the inner surface are smaller than the diameters of pores in the outer surface; (c) the following relationship is satis fied: 0.001 [μm] ≤ dIS ≤ [μm], wherein dIS is the average diameter of the pores at the inner surface; (d) the porosity increases from the inner surface toward the outer surface, and then decreases from at least one portion having a maximum porosity, of the wall section of the membrane, toward the outer surface; and (e) the hollow fiber membrane has a relationship of 2 [%] ≤ DR ≤ 20 [%], wherein DR [%] is the portion of the pores in the inner surface with a diameter exceeding φ max, and φ max [μm] is the critical diameter of a monodispers polystyrene latex to be removed, found by a fine particle-passing test, wherein the monodispers polystyrene latex is a suspension, the concentration of the stock solution being 10 w/v %, diluted with an aqueous solution of 0.1 % by vol. of Polyoxyethylen -sorbitan-monolaurate to a concentration of the polystyrene latex suspension of 0.01 w/v % which is referred to as PLS below, wherein the critical diameter of a particle to be removed (φ max) is defined as the minimum particle diameter of the monodispers polystyrene latex inducing a relationship of Rj ≥ 95%, wherein Rj is a polystyrene latex-rejection calculated by the following equation: Rj % = 100 × ApPSt − Apt / AfPSt − AfT wherein ApPSt is the absorbance of the filtrate of the PLS at 250 nm; ApT is the absorbance of the filtrate of the aqueous solution of 0.1% by vol. of the Polyoxyethylen -sorbitan-monolaurate at 250 nm; AfPSt is the absorbance of the PLS as introduced into a miniature module at 250 nm; and AfT is the absorbance of the aqueous solution of 0.1% by vol. of Polyoxyethylen -sorbitan-monolaurate at 250 nm; wherein a pore diameter is calculated by using the following equation: the pore diameter μm = the pore area / π 1 / 2 × 2 wherein the pore area is analyzed using an image analysis software with a scanning electron microscope photograph of the inner surface to create a histogram and to summarize it as a pore distribution; and DR [%] is determined as that portion of pores with dIS exceeding φ max (a) the hollow fiber membrane has skin layers on its inner and outer surfaces; wherein the portion on the rear sides of the skin layers is a sponge-like support layer having pores with larger diameters and a higher porosity than those of the skin layers; (b) the diameters of pores in the inner surface are smaller than the diameters of pores in the outer surface; (c) the following relationship is satis fied: 0.001 [μm] ≤ dIS ≤ [μm], wherein dIS is the average diameter of the pores at the inner surface; 0.001 [μm] ≤ dIS ≤ [μm], wherein dIS is the average diameter of the pores at the inner surface; (d) the porosity increases from the inner surface toward the outer surface, and then decreases from at least one portion having a maximum porosity, of the wall section of the membrane, toward the outer surface; and (e) the hollow fiber membrane has a relationship of 2 [%] ≤ DR ≤ 20 [%], wherein DR [%] is the portion of the pores in the inner surface with a diameter exceeding φ max, and φ max [μm] is the critical diameter of a monodispers polystyrene latex to be removed, found by a fine particle-passing test, wherein the monodispers polystyrene latex is a suspension, the concentration of the stock solution being 10 w/v %, diluted with an aqueous solution of 0.1 % by vol. of Polyoxyethylen -sorbitan-monolaurate to a concentration of the polystyrene latex suspension of 0.01 w/v % which is referred to as PLS below, 2 [%] ≤ DR ≤ 20 [%], wherein DR [%] is the portion of the pores in the inner surface with a diameter exceeding φ max, and φ max [μm] is the critical diameter of a monodispers polystyrene latex to be removed, found by a fine particle-passing test, wherein the monodispers polystyrene latex is a suspension, the concentration of the stock solution being 10 w/v %, diluted with an aqueous solution of 0.1 % by vol. of Polyoxyethylen -sorbitan-monolaurate to a concentration of the polystyrene latex suspension of 0.01 w/v % which is referred to as PLS below,