 A novel porous polymer membrane based on polyhedral oligomeric silsesquioxane (POSS) composite poly(acrylonitrile–maleic anhydride) (P(AN–MAH)) is prepared by phase inversion method, and corresponding P(AN–MAH) composite gel polymer electrolyte (GPE) is prepared by further absorbing the liquid electrolyte. The structure of the prepared POSS and P(AN–MAH), and the properties of the composite P(AN–MAH) membranes and GPEs are investigated. The results indicate that the introduction of POSS significantly reduces the crystallinity of P(AN–MAH), which gives the composite membrane and GPE excellent performance. Compared with pure P(AN–MAH)-based membrane and GPE, the composite membrane containing 5 wt% POSS exhibits the best porosity (69.9%) and electrolyte uptake (311.9 wt%), and the most excellent electrochemical performance is also presented by the corresponding GPE: enhanced ionic conductivity of 2.51 × 10−3 S cm−1 at room temperature; better compatibility with electrode; significantly increased lithium-ion transference number of 0.53; a remarkably widened electrochemical stability window of 5.6 V (vs. Li/Li+); a higher discharge specific capacity of 147 mAh g−1 with a Li/GPE-5%/LiFePO4 cell at 0.2 C.