In this research, an approximated technique is proposed for predicting the performance of membrane gas separation using an asymmetric membrane-based gas separator. The permeation behavior of the high-flux asymmetric membrane varies from that of the traditional symmetric membrane. The advanced mathematical model has been applied in this study for the separation of a binary gas mixture. In the present work, a shell-fed hollow fiber module like counter-current flow pattern is modeled mathematically for CO2 separation from CH4. Finite Difference method (FDM) is applied to solving the equations numerically. The models offered separation for a membrane module, for given gas conditions, simulating permeate and residue composition and the stage cut. The different parameters are investigating like a change in the pressure ratio, stage cut and feed flow rates. The numerical approach is helpful as it entails the least effort and computational time due to the fact algebraic equations are used instead of differential equations. The obtained model’s data also verified with numerical and experimental results available in the literature.