The present invention readily provides an electrolyte which is capable of suppressing elution of a radical-quenching material from the electrolyte and has high proton conductivity and excellent durability.The polyelectrolyte is obtainable by chemically bonding a proton-conducting polymer having protonic acid groups to a radical-quenching material having a radical-scavenging capability via moieties other than the protonic acid groups by heating at a temperature of 60° C. or more and 250° C. or less. The proton-conducting polymer is an aromatic polymer, polyether ketone or a polyether ether ketone, or phenol resin, has a sulfonic acid group, and has a hydrogen ion exchange capacity of 0.5 meq/g or more and 10 meq/g or less. The radical-quenching material has at least one methylol group in the molecule.