The idea of CO2 capture was proposed through a multistep vacuum swing adsorption (VSA) process from the tail gas of a hydrogen purification unit with the composition of H-2, 25%; CO2, 55%; CH4, 17%; CO, 1%; and N-2, 2 mol %, using a SAPO-34 molecular sieve. The experimental isotherms and dynamic breakthrough curves were obtained on the lab scale to estimate the equilibrium and kinetic parameters of the adsorption. The VSA process was designed and simulated on the basis of dynamic adsorption-desorption mass and energy balances in the gas and solid phases. Then, the purity of the desorbed CO2, the recovery of CO2, and the productivity of the process with energy consumption were determined at the cyclic steady state condition. The operational conditions such as weight-hourly space velocity (WHSV), feed pressure, vacuum pressure, and purge to feed ratio were investigated and optimized by the method of fractional factorial design to achieve 90% CO2 purity with more than 70% recovery. The simulation process was performed with conventional adsorbents of activated carbon (AC) and zeolite SA and the results revealed the priority of SAPO-34 against AC and SA for CO2 enrichment.