The sequestration of carbon dioxide (CO2) emitted from industrial flue gas streams is one of important measures to stabilize greenhouse gas concentrations in the atmosphere to fulfill the objective of UNFCCC. This project proposes an integrated system that utilizes membrane contactors for gas absorption in aiming to accomplish CO2 capture. The absorption efficiency of CO2 in ethanolamine (MEA) solvent system of a parallel-plate membrane contactor with both concurrent- and countercurrent-flow operations was investigated theoretically and experimentally to predict concentration distributions, mass transfer coefficient and gas absorption rates. A two-dimensional mathematical modeling for predicting the concentration distribution and total absorption rate was developed, and the analytical solution for the resultant partial differential equations is obtained using the separated variables method with an orthogonal expansion technique. An experimental system with CO2/N2 gas mixture and Amine solutions as absorbents divided with a PTFE (Polytetrafluoroethylene) membrane system is used as the gas absorption membrane modules to conduct CO2 absorption performance tests. The theoretical predictions of the absorption efficiency, total absorption rate, average Sherwood number and concentration distributions were presented graphically with the mass-transfer Graetz number, inlet CO2 concentration, and both gas feed and absorbent flow rates as parameters. Four types of membrane cartridges, namely the parallel-plate module, parallel-plate module with carbon-fiber channel, hollow fiber module and spiral helix, were proposed in the present study to conduct the CO2 absorption performances in each individual design of the membrane contactor systems. Moreover, the operating and designing parameters that affect the CO2 absorption performance will be investigated to conclude a set of optimal operating conditions for the proposed gas-liquid membrane contactor systems.