This invention is to provide a macromolecular solid electrolyte exhibiting high ion conductivity even at low temperatures and a polymer used therefor. This invention relates to a polymer formed of structural units represented by the following formula (1): ##STR1## wherein R represents a linear or branched alkylene residue of 1 to 4 carbon atoms; X.sup.- represents a deprotonated residue of an acid; Y.sup.+ represents a cation of a nitrogen-containing compound; Z represents a residue of a monoethylenically unsaturated compound; m represents a number of average addition mols of a branched chain bound to the structural unit, --(RO)--, forming a main chain and is in the range of 2 to 20; n is in the range of 3 to 500; and p is in the range of 0 to 2, and macromolecular solid electrolyte comprising the polymer as an essential component.