A method by which unstable groups of a melt-processable fluoropolymer can be stabilized rapidly and efficiently. The resultant stabilized polymer through melt molding gives a molded article free from not only air inclusions or voids but also discoloration. The method is characterized by melt-kneading a melt-processable fluoropolymer having unstable groups in a kneader having a stabilization zone satisfying the following requirements: (1) an oxygen-containing gas is present in the stabilization zone and (2) water is present in that zone. Preferably, (3) the absolute pressure in the zone is regulated to 0.2 MPa or higher; or (a) an oxygen-containing gas is present in the zone in an amount sufficient to enable the stabilized fluoropolymer to have a carbon radical spin number of 5x1013 spins/g or smaller as determined by electron spin resonance (ESR) spectroscopy at a temperature of 77 K and (b) water is present in that zone.