PSA-SPUR (Pressure Swing Adsorption with Selective Purge Gas Recirculation) has been developed aimed at separating the most strongly adsorbing component from a gas mixture at high product purity and recovery. The innovative strategy for designing a Pressure Swing Adsorption system features recycling its purge gas stream exiting the column and mixing it back into the feed. This operation enriches the mixed feed with an elevated fraction of the heavy component during the adsorption step, thus enhancing the PSA’s performance greatly. Reusing the purge gas helps significantly increase the product recovery compared to conventional methods where purge gas is simply discarded or taken as a low-quality product. For theoretical analysis of a PSA-SPUR system, a bespoke Equilibrium Theory model was developed and solved successfully, providing valuable insights into the performance of the PSA-SPUR system designed for capturing CO2 from a flue gas. The study revealed that there exists an optimum extent of purging that maximises the heavy component mole fraction in the mixed feed, leading to the best possible feed throughput of the adsorption system. Furthermore, the effects of the desorption pressure and feed composition on the PSA-SPUR system’s performance were investigated. The results indicate that the CO2 capture PSA-SPUR system using commercial zeolite 13X has excellent potential to achieve very high product purity and recovery, being allowed to operate at moderate vacuum pressures without having to compress the flue gas feed, even when the gas feed contains less than 10 mol% CO2.