The present invention provides a polymer solid electrolyte excellent in thermal properties, physical properties and ion conductivity and being close to practical level; especially, a totally solid electrolyte and a composition for producing the same. A composition for polymer solid electrolyte includes a copolymer having repeating units represented by Formula (I): ##STR00001## (wherein each of R.sub.1 to R.sub.3 independently represents a hydrogen atom or a C1-C10 hydrocarbon group; R.sub.4a and R.sub.4b independently represents a hydrogen atom or a methyl group; R.sub.5 represents a hydrogen atom, a hydrocarbon group, an acyl group or a silyl group; and m is an integer of 1 to 100), and repeating units represented by Formula (II): ##STR00002## (wherein each of R.sub.6 and R.sub.8 independently represents a hydrogen atom or a C1-C10 hydrocarbon group; R.sub.9 represents an organic group having at lease one functional group selected from the group consisting of hydroxyl group, carboxyl group, epoxy group, acid anhydride group and amino group); and an electrolyte salt.