The effects of addition of an ionic liquid to pure water as a physical absorbent and monoethanolamine (MEA) solutions as a chemical absorbent on carbon dioxide (CO2) absorption through hollow fiber membrane contactors were investigated using a 2D axisymmetric model. A numerical simulation was developed based on finite element method using computational fluid dynamics techniques. Liquid phase flowed in the tube side and gas mixture containing CO2 passed in the shell side of the membrane contactor in co-current and countercurrent modes. The simulation results are consistent with experimental data, and the root-mean-square error was calculated as 9 and 13% for pure water and 25 wt % for ionic liquid solution. The results showed that addition of 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]) to the base fluids increases CO2 absorption in both physical and chemical absorbents. However, the effects of an ionic liquid in physical absorption is higher than that in chemical absorption. Addition of 10 wt % [Bmim][BF4] to 3.5 wt % MEA solution could increase the absorption rate by 12% in countercurrent flow compared to a 6 wt % MEA solution without [Bmim][BF4] despite lower MEA concentration. Also, the results indicate that reaction term in a chemical absorbent is more important in low liquid flow rates. It can also be found that addition of 25 and 50 wt % of [Bmim][BF4] to pure water can enhance absorption performance up to 30 and 75%.