Global warming has become more and more serious, which is caused by greenhouse gases. Therefore, decreasing the emission of CO2 has become an important research topic in the world. This study aimed to utilize a pressure swing adsorption (PSA) process to capture CO2 from synthesis gas, which is the effluent stream of water-gas-shift reactor. The PSA process studied is a single-bed four-step process at mid-high temperature using K 2CO3-promoted hydrotalcite. The feed gas entering the PSA process consists of 27 % H2O, 5 % CO, 28 % CO2 and 40 % H2. It uses the method of lines combined with upwind differences, cubic spline approximation and LSODE of ODEPACK software to solve the equations. The optimal operating condition is obtained by varying the operating variables, such as feed pressure, bed length, etc. Furthermore, single-bed four-step process could achieve 98.49% recovery of H2 as the top product and 96.42% purity and 96.57% recovery of CO2 as the bottom product.