A numerical analysis was performed to investigate the removal behavior of carbon dioxide using a hollow fiber membrane contactor in which an aqueous potassium carbonate solution flows as an absorbent. An important feature is the inclusion of the nonlinear reversible reaction terms that result from the reactions between the absorbent solution and carbon dioxide. The coupled nonlinear partial differential equations were derived and solved numerically, which describe either the absorption or desorption of carbon dioxide in a membrane contactor. In a numerical analysis, the absorbent liquid always flows through the inner side of the hollow fiber in both absorption and desorption steps. The analysis includes the effects of the pressure of feed gases and the extent of vacuum, the absorbent flow rates, the concentration of potassium carbonate in an absorbent solution, the diameter and length of the fibers. One important result is the determination of the optimal absorbent flow rate such that it is saturated just at the exit of the contactor.