Coalbed methane (CBM) is an unconventional natural gas, and vigorous development of CBM has great significance for improving the current status of global coal mine safety production, alleviating market gas supply pressure, and protecting the ecological environment. CBM mainly consists of CH, CO and a small amount of HS. In order to improve the comprehensive energy utilization efficiency of CBM, it is necessary to capture both CO and HS from CBM. In this paper, a comprehensive 2D model was established by COMSOL Multiphysics for simultaneously removing CO and HS in CBM. The KCO/potassium lysinate (PL) mixed solution was employed as the absorbent in a membrane contactor. The impacts of gas and liquid velocities, liquid concentration and temperature on the absorbent performance were studied. The results obtained by using the simulated membrane contactor were consistent with the experimental data in the literature. The results indicate that the gas velocity was the most significant influential factor to the gases removal efficiency. Furthermore, it was concluded that the KCO/PL mixed solution had a better decarburization performance than the single KCO solution. The optimal operating conditions for simultaneous removal process by using KCO/PL mixed solution were obtained by response surface method. More importantly, the blends of amino acid salts and carbonate solution have great prospects in the membrane absorption of acid gases from CBM.