The present invention provides a fluoropolymer containing fluorosulfonyl groups capable of forming a polymer electrolyte membrane with high conductivity and hot water resistance, a method for its production, a fluoropolymer containing acid-form sulfonic acid groups and a method for its production, a polymer electrolyte membrane, a membrane-electrode assembly and a polymer electrolyte fuel cell. The method for producing a fluoropolymer containing fluorosulfonyl groups of the present invention comprises copolymerizing a monomer m1 (CF2═CFCF2O-Q1-SO2F) and TFE in a reactor at a temperature of from 150 to 200° C. in the presence of a radical polymerization initiator, wherein the radical polymerization initiator is continuously or sequentially added into the reactor so that the concentration of the radical polymerization initiator is kept to at most 2.5 mass ppm of the initial feed of the monomer m1 present in the reactor before initiation of the copolymerization during the copolymerization, and the molar ratio of the total feed of the monomer m1 to the total feed of tetrafluoroethylene is from 1.5 to 20