The pressure swing adsorption (PSA) process was used to capture carbon dioxide (CO2) from the flue gas of a coal-fired power plant to reduce CO2 emissions. Herein, CO2 was captured from flue gas using the PSA process for at least 85 vol% CO2 purity and with the other exit stream from the process of more than 90 vol% N2 purity. The extended Langmuir–Freundlich isotherm was used for calculating the equilibrium adsorption capacity, and the linear driving force model was used to describe the gas adsorption kinetics. We compared the results of breakthrough curves obtained through experiments and simulations to verify the accuracy of the mass transfer coefficient. The flue gas obtained after desulphurization and water removal (13.5 vol% CO2 and 86.5 vol% N2) from a subcritical 1-kW coal-fired power plant served as the feed for the designed three-bed, nine-step PSA process. To determine optimal operating conditions for the process, the central composite design (CCD) was used. After CCD analysis, optimal operating conditions with a feed pressure of 3.66 atm and a vacuum pressure of 0.05 atm were obtained to produce a bottom product with a CO2 purity of 89.20 vol% and a recovery of 88.20%, and a top product with a N2 purity of 98.49 vol% and a recovery of 93.56%. The mechanical energy consumption was estimated to be 1.17 GJ/t-CO2.