A novel gel polymer electrolyte (GPE), based on poly(methyl methacrylate–acrylonitrile–ethyl acrylate) (P(MMA–AN–EA)) terpolymer, is designed to match LiNi0.5Mn1.5O4 cathode of 5 V lithium ion battery. The performances of the synthesized P(MMA–AN–EA) terpolymer and the corresponding membrane and GPE are investigated by scanning electron microscope, energy dispersive spectroscopy, nuclear magnetic resonance spectra, Fourier transform infrared spectra, thermogravimetric analyzer, electrochemical impedance spectroscopy, linear sweep voltammetry, and charge/discharge test. It is found that the pore structure of P(MMA–AN–EA) membrane is affected by the dose of pore forming agent, polyethylene glycol (PEG400). The membrane with 3 wt% PEG400 presents the best pore structure, in which pores are dispersed uniformly and interconnected, and exhibits the largest electrolyte uptake, resulting in the highest ionic conductivity of 3.82 × 10−3 S cm−1 for the corresponding GPE at room temperature. The GPE has improved compatibility with lithium anode and is electrochemically stable up to 5.2 V (vs. Li/Li+). The high voltage LiNi0.5Mn1.5O4 cathode using the resulting GPE exhibits excellent cyclic stability, maintaining 97.9% of its initial discharge capacity after 100 cycles compared to that of 79.7% for the liquid electrolyte at 0.5 C.