An electrolytic membrane comprising a porous membrane substrate containing a cross-linked polymer electrolyte having at least a structural component shown by following chemical formula 1: wherein A represents a repeating unit having an aromatic hydrocarbon group substituted by at least a sulfonic acid group, B represents a repeating unit having one of a nitrogen-containing hetero ring compound residue, and the sulfate, hydrochloride or organic sulfonate thereof, C represents a repeating unit having a cross-linked group, and X, Y and Z represent mol fractions of respective repeating units in the chemical formula 1, with 0.34≦X≦0.985, 0.005≦Y≦0.49, 0.01≦Z≦0.495 and Y≦X and Z≦X, provided that, in the repeating unit A, a ratio of the aromatic hydrocarbon group substituted by at least a sulfonic acid group is 0.3 to 1.0, and the number of the sulfonic acid group in the aromatic hydrocarbon group is 1 to 3.