This paper presents the mass transfer simulation of the gas absorption process in a hollow-fiber membrane contactor by means of the finite element method. Theoretical mass transfer simulations were performed in order to describe the absorption of CO₂ by distilled water as well as aqueous solutions of diethanolamine. The simulations were focused on the behavior of gas and liquid phases in order to obtain the distribution of CO₂ and absorbent concentrations along the length of the membrane contactor. The effect of the operating parameters and membrane physical properties on the performance of the contactor was investigated. Validation of the applied simulation method, was made through comparing the calculated flux of CO₂ absorption with the experimental data reported in literature for a Celgard MiniModule. The obtained simulation results, which are in good agreement with the experimental values for different liquid velocities, reveal that the removal of CO₂ increases with porosity/tortuosity ratio and decreases with the inner diameter of the fibers. It is indicated that the proposed model well predicts the absorption mass transfer in the hollow-fiber membrane contactors.