PURPOSE: A treating agent forming a complex with copper is added to the coagulation bath or the formed fiber is treated with the agent after the coagulation, thus producing the titled hollow fiber with a copper concentration of less than a specific level in the absolutely dried fiber.

CONSTITUTION: The spinning dope is extruded through annular nozzles, coagulated in an aqueous caustic soda, washed with water and dried to produce hollow fiber by the cuprammonium method. When the resultant fiber is applied to an artificial kidney, a treating agent that forms a complex with copper is added to the coagulation bath or the fiber is treated with the agent after coagulation. Thus, the concentration of copper is reduced to lower than 5ppm in the hollow fiber. The agent forming a complex with copper is preferably selected from the group consisting of glycerol, tartaric acid, ethylenediamine, propylenediamine, ethylene glycol, propylene glycol, low molecular weight polyethylene glycol, and low molecular weight polypropylene glycol.