A multi-stage model is developed for CO2 separation by hollow-fiber membrane. The model permits rapid solution of the governing differential mass and pressure distribution in hollow-fiber gas separation modules using a computational scheme that does not rely on commercial software and conventional numerical methods such as shooting techniques. For 1-stage, 2-stage and 3-stage configurations the changes of required separation areas according to stage cuts are computed. A simple model predictive control technique is employed to provide optimal operation conditions based on the proposed model. Values of stage cuts can easily be identified for various desired mole fractions and recovery rates. From the results of numerical simulations, we can see that the proposed model can be effectively used in the control of gas separation process by hollow-fiber membrane modules.