A porous hollow fiber membrane containing a vinylidene fluoride-based resin, characterized by : having a gradient structure in which a pore diameter of pores in the hollow fiber membrane gradually becomes smaller at least toward one of inner and outer peripheral surface sides; and being hydrophilized by containing a crosslinked body of a polyvinylpyrrolidone-based resin, wherein a content of the crosslinked body which is measured as set out in the description is 0.1 mass % or higher and lower than 15 mass %, a K-value of the polyvinylpyrrolidone-based resin is 30 to 120, wherein the K-value is determined as disclosed in the description, the hollow fiber membrane is composed of a single layer, the crosslinked body is obtained by crosslinking the polyvinylpyrrolidone-based resin contained in the hollow-fiber-membrane-before-crosslinking, the water permeation rate at an inter-membrane differential pressure of 0.1 Mpa is 3000 to 40000 L/m 2 /hr; a fractionation particle diameter which is measured as set out in the description is 0.001 to 0.5 μm, a ratio FD10/FW of a pure water permeation speed FD10 at an inter-membrane differential pressure of 0.1 MPa in the dry state after wet and dry states are alternately repeated ten times, to a pure water permeation speed FW at an inter-membrane differential pressure of 0.1 MPa in the wet state, is 40% or higher, a ratio of the inner peripheral side fine pore diameter to the outer peripheral side fine pore diameter is 30 to 50 wherein the pore diameter ratio is measured as set out in the description and, the pure water permeability coefficient of the hollow fiber membrane is 0.4×10 -11 ×L (m 2 ) or larger and 6×10 -11 ×L (m 2 ) or smaller, when the thickness of the hollow fiber membrane is L (m), wherein the pure water permeation speed and the pure water permeability coefficient are measured at a temperature of 25°C. having a gradient structure in which a pore diameter of pores in the hollow fiber membrane gradually becomes smaller at least toward one of inner and outer peripheral surface sides; and being hydrophilized by containing a crosslinked body of a polyvinylpyrrolidone-based resin, wherein a content of the crosslinked body which is measured as set out in the description is 0.1 mass % or higher and lower than 15 mass %, a K-value of the polyvinylpyrrolidone-based resin is 30 to 120, wherein the K-value is determined as disclosed in the description, the hollow fiber membrane is composed of a single layer, the crosslinked body is obtained by crosslinking the polyvinylpyrrolidone-based resin contained in the hollow-fiber-membrane-before-crosslinking, the water permeation rate at an inter-membrane differential pressure of 0.1 Mpa is 3000 to 40000 L/m 2 /hr; a fractionation particle diameter which is measured as set out in the description is 0.001 to 0.5 μm, a ratio FD10/FW of a pure water permeation speed FD10 at an inter-membrane differential pressure of 0.1 MPa in the dry state after wet and dry states are alternately repeated ten times, to a pure water permeation speed FW at an inter-membrane differential pressure of 0.1 MPa in the wet state, is 40% or higher, a ratio of the inner peripheral side fine pore diameter to the outer peripheral side fine pore diameter is 30 to 50 wherein the pore diameter ratio is measured as set out in the description and, the pure water permeability coefficient of the hollow fiber membrane is 0.4×10 -11 ×L (m 2 ) or larger and 6×10 -11 ×L (m 2 ) or smaller, when the thickness of the hollow fiber membrane is L (m), wherein the pure water permeation speed and the pure water permeability coefficient are measured at a temperature of 25°C. <EOS>