This study reports the separation of pure hydrogen (H2) employing pressure swing adsorption (PSA). The Li-X and Li-hierarchical X (Li–H-X) zeolite were prepared by an ion exchange process. The sorbents were evaluated through several experiments including, breakthrough, empty bed contact time (EBCT), single-bed, and two-bed PSA with different steps. The effect of pressure, purity, and recovery relationship was developed. The high-pressure PSA study was performed at 4, 6, and 10 bar with varying feed flow rates to assess their efficacy in pure H2 separation using binary gas stream (H2/CO2, 75/25 vol.%). The breakthrough adsorption capacity of Li–H-X exhibited 3.4 mmol g−1 and 0.212 mmol g−1 of CO2 and H2, respectively. Li–H-X shows ∼8% higher CO2 sorption capacity than the Li-X sorbent at 1 bar and 300 K due to the large meso-microporous structure of the sorbent. The two-bed PSA purity and recovery were found higher than single-bed PSA. Using two-bed PSA, the Li–H-X achieved a 99.5% of purity, 92.9% of recovery, and 10.4 mL min−1 g−1 of productivity, which was ∼16% higher recovery and productivity than single-bed PSA at a flow rate of 1200 mL min−1 at 6 bar. With increasing the pressure and flow rate, the recovery of Li–H-X was enhanced up to 93.7% with 99.1%–99.9% H2 purity. The long-term PSA was run using Li–H-X sorbent for 7.5 h with 230 cycles with H2 purity between 98.5 and 99.5% at 6 bar. Interestingly, the adsorbent shows the scalability of PSA for efficient H2 separation for a binary mixture of H2/CO2.