To prepare a polymeric solid electrolyte, which has an excellent discharge characteristic and is suitable as an electrolyte of a lithium secondary cell, within a short time in an efficient manner.

For the preparation of a polymeric solid electrolyte by polymerizing a polyalkylene glycol monomer having an ethylenically unsaturated double bond in the presence of a lithium salt and a solvent, a peroxy ester of the following formula is also present (wherein R1 to R3 independently represent a hydrogen atom or a hydrocarbon residue; and R4 to R6 independently represent an alkyl group or aryl provided that at least one of R4 to R6 represents an alkyl group having 2 or more carbon atoms or an aryl group).