The CO2 absorption with the use of amine solution flowing through the shell side of the hollow fiber membrane contactor under both concurrent-flow and countercurrent-flow operations was investigated experimentally and theoretically. An one-dimensional mathematical modelling equation for predicting the absorption rate under various absorbent flow rate, CO2 feed flow rate and inlet CO2 concentration in the gas feed was solved numerically using the fourth Runge–Kutta method with the shooting strategy. The correlated equation of the average Sherwood number in predicting the mass transfer coefficient of the CO2 absorption of the hollow-fiber membrane contactor was obtained. The theoretical predictions showed that a considerable improvement of the CO2 absorption rate was achieved and validated by experimental results within acceptable accuracy. In this study the mass-transfer coefficient correlation equation with the number of fibers as a parameter was developed; an one-dimensional mathematical model was derived and solved for the CO2 absorption efficiency in hollow-fiber membrane modules; and lastly the effects of various operation parameters on the CO2 absorption rate was found theoretically and validated experimentally.