Carbon capture and storage (CCS) has been identified as an essential technology to meet the internationally agreed goal of limiting the temperature increase to 2 °C. Compared to traditional gas-liquid contactors, the membrane contactors provide many beneficial features, including the high specific area, independent gas and liquid flows, modular units and easy to include internal heat exchange. The solvent carbon dioxide absorption processes employing membrane contactors is an important technology. Limited by the low partial pressure of carbon dioxide, physical absorption is not a feasible technology for post-combustion flue gas treatment. However, chemical absorption technology is high energy consumption. In this study, an innovative hybrid absorption/stripping membrane contactor (HASMC) for physical solvent carbon capture is proposed. The simultaneous absorption and stripping can enhance the effectiveness of carbon capture. The device can raise the feasibility of applying physical solvent technology to the treatment of gases with low carbon dioxide partial pressure. In this paper, computational fluid dynamics simulation of the concentration profiles and mass fluxes for parallel-flow and cross-flow modules are presented.