Composite polymer electrolyte (CPE) membranes, comprising poly(vinylidene fluoride–hexafluoropropylene) (PVdF–HFP), aluminum oxyhydroxide (AlO[OH] n ) of two different sizes 7μm/14nm and LiN(C2F5SO2)2 as the lithium salt were prepared using a solution casting technique. The prepared membranes were subjected to XRD, impedance spectroscopy, compatibility and transport number studies. Also Li Cr0.01Mn1.99O4/CPE/Li cells were assembled and their charge–discharge profiles made at 70°C. The incorporation of nanofiller greatly enhanced the ionic conductivity and the compatibility of the composite polymer electrolyte. The film which possesses a nanosized filler offered better electrochemical properties than a film with micron sized fillers. The results are discussed based on Lewis acid–base theory.