It is intended to provide a blood purifier which has a high water permeability and is used for the treatment of chronic renal failure, characterized in that the performance thereof in the treatment is not affected by patient's conditions. The invention is directed to a hollow fiber membrane with excellent performance stability in which an average membrane thickness is 10 [mu]m or more and 50 [mu]m or less and an average pore radius is 150 AA or more and 300 AA or less, characterized in that the permeability of pure water at 37 DEG C is 150 mL/m<2>/hr/mmHg or more and 1500 mL/m<2>/hr/mmHg or less and the ratio of the overall mass transfer coefficient of plasma solution of ss2-microglobulin (Koss2) to the overall mass transfer coefficient of aqueous solution of myoglobin (Komyo) (Koss2/Komyo) is 0.7 or more and 1.0 or less.