Nanocomposite polymer electrolyte membranes (NCPEMs) based on poly(acrylic acid)(PAA) and titania (TiO2) are prepared by a solution casting technique. The ionic conductivity of NCPEMs increases with the weight ratio of TiO2.The highest ionic conductivity of (8.36 ± 0.01) × 10−4 S·cm−1 is obtained with addition of 6 wt % of TiO2 at ambient temperature. The complexation between PAA, LiTFSI and TiO2 is discussed in Attenuated total reflectance-Fourier Transform Infrared (ATR-FTIR) studies. Electrical double layer capacitors (EDLCs) are fabricated using the filler-free polymer electrolyte or the most conducting NCPEM and carbon-based electrodes. The electrochemical performances of fabricated EDLCs are studied through cyclic voltammetry (CV) and galvanostatic charge-discharge studies. EDLC comprising NCPEM shows the specific capacitance of 28.56 F·g−1 (or equivalent to 29.54 mF·cm−2) with excellent electrochemical stability.