We prepare an all solid-state, liquid-free, polymer electrolyte (ASPE) from a lithium salt and a graft copolymer consisting of a polyimide main chain and poly(ethylene glycol) methyl ether methacrylate side chains using atom transfer radical polymerization method. The ionic conductivity of ASPEs increases with increasing the side chain length. The ionic conductivity of the ASPE whose POEM content=60wt% shows 6.5×10−6 S/cm at 25°C. The ASPEs having shorter average distance between side chains and/or shorter side chain length show higher mechanical strength. The tensile strength of the ASPEs is more than 10MPa and about 20 times higher than that of the ASPEs in the previous study [Electrochim. Acta, 50 (1998) 3832]; hence, the ASPEs have sufficiently high mechanical strength for a polymer electrolyte of lithium secondary batteries.