The development of light weight and compact hydrogen storage materials is still prerequisite to fuel-cell technology to be fully competitive. The present experimental study reports the hydrogen storage capability of sulfonated poly-ether-ether-ketone (SPEEK)-hexagonal boron nitride (h-BN) (SPEEK-h-BN) nanocomposite membranes. The nanocomposite membranes are prepared by considering various amount of h-BN (0, 1, 3 and 5 wt. %) by phase inversion technique. The degree of sulfonation of the PEEK (SPEEK) is found to be 65% by Proton Nuclear Magnetic Resonance (1H NMR) spectroscopy. Hydrogen adsorption studies have been carried out using a Seiverts-like hydrogenation setup. The membranes are characterized by X-ray Diffractometer (XRD), Micro-Raman spectroscopy, Fourier Transform Infrared (FTIR) spectroscopy, Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM), CHN-elemental analysis and Thermo Gravimetric Analysis (TGA). It is observed that the SPEEK-5% h-BN membrane performs better than pure SPEEK membrane, has maximum storage capacity of 2.98 wt. % at 150 °C and the adsorbed hydrogen has an average binding energy of 0.38 eV. The TGA study shows the dehydrogenation behavior of hydrogenated SPEEK-h-BN nanocomposite membrane and it is found to be in the temperature range of 214–218 °C for SPEEK-5% h-BN membrane