A process for producing a functional membrane comprising an ion irradiation step in which a polymeric film base is irradiated with high-energy heavy ions at a density of 104 to 1014 particles/cm2 to generate active species in the film base; and, subsequent to the ion irradiation step, a graft polymerization step in which at least one monomer selected from the members of group A which are monomers each having a functional group and 1 to 80 mol% (based on the total amount of the monomer(s) of group A) of a monomer selected from the members of group B which are crosslinking agents for the monomers of group A are added to the film base and graft polymerization of the film base and the monomers are then performed; and a functional membrane produced by the process. By employing this process, it becomes possible to produce a functional membrane which combines high functionality with gas-barrier property inherent in a polymeric film base. In particular, a polymeric electrolyte membrane having high proton conductivity and good gas barrier property can be produced, which is highly suitable as a polymeric electrolyte membrane for a fuel cell.