A topological structural polymer is designed and synthesized by sequential living polymerization of pinacol vinylboronate and poly(ethylene glycol) methyl ether methacrylate using hyperbranched polystyrene as the core. The as-synthesized polymer containing lithium salt is casted onto the ceramic electrostatic spinning film to prepare the composite solid polymer electrolyte. As predicted, the electrolyte shows a high ionic conductivity of 9.63 × 10−5 S cm−1 at room temperature, which likely due to the creation of conductive network on the surfaces of the nanowires. In addition, introduction of poly(pinacol vinylboronate) segments onto the hyperbranched polymer strongly improves the electrochemical stability (reaches 5.2 V) of the electrolyte in comparison to the one without poly(pinacol vinylboronate) chains. As a result, the LiFeO4/Li cell using the electrolyte presents excellent long cycle stability at 50 °C (average discharge capacity of 130 mA h g−1 with coulombic efficiency close to 100% over 800 cycles at 0.5 C) as well as very good cell performance at room temperature (discharge capacity reaches 162 mAh g−1 with average coulombic efficiency of ∼100%). More importantly, we also confirm that the electrolyte can be applied to high-voltage cathode materials, such as LiCoO2 and Li1.2Mn0.5Ni0.2O2-based cathodes, which also shows satisfactory cell performance.