A polymer electrolyte extends the cycle life, improves the safety, and reduces the swelling of a battery, compared with a polymer electrolyte containing a poly(alkylene oxide) polymer. Also, a lithium battery utilizes the polymer electrolyte. The polymer electrolyte contains a polymerized product from a polymer electrolyte forming composition containing a multifunctional isocyanurate monomer of a particular structure, a lithium salt, and a non-aqueous organic solvent.