The development of safe and long-term stable solid polymer electrolytes is a major challenge for all solid-state batteries because good interfacial stability toward electrodes is the main concern. In this paper, a triblock copolymer polystyrene-poly(ethylene glycol)-polystyrene (PS-PEG-PS) is synthesized and investigated as solid polymer electrolyte. This polymer electrolyte exhibits a high ionic conductivity of 1.1 x 10(-3) S cm(-1) at 70 degrees C, transference number of 0.17, high degree flexibility, good mechanical strength and thermal stability. The interface stability of the solid-polymer electrolyte is investigated in Li metal cell and the comprehensive electrochemical properties are studied in cells with either LiFePO4 or LiNi0.5Co0.3Mn0.2O2 cathode materials. Good rate capability and excellent cyclability of the solid polymer electrolyte is demonstrated, with an electrochemical stability window extending above 4.5 V vs. Li+/Li. Furthermore, constant voltage impedance measurements give evidence of the better interface stability and rate capability of LiNi0.5Co0.3Mn0.2O2//Li battery. Meanwhile, molecular orbital energy levels calculated by density functional theory are consistent with experiments.