The present invention provides a polymer electrolyte material comprising a polymer having a repeating unit based on an alicyclic fluoromonomer having a carbon-carbon double bond with radical polymerization reactivity, wherein either of carbon atoms at both ends of the double bond constitutes a ring structure; the repeating unit contains a strongly acidic group such as a sulfonic acid group; the polymer is preferably perfluorinated. This electrolyte material has a high softening temperature and a polymer electrolyte fuel cell using this electrolyte material can be operated at higher temperatures than before. Furthermore, when this electrolyte material is used for a catalyst layer of a cathode in a polymer electrolyte fuel cell, an output voltage of the cell can be increased.