The mu VT-NEMD method, a combination of the mu VT-MC and the boundary-driven non-equilibrium MD, has been applied for simulating permeation of pure- and mixed-gases through membranes with slit-like pores under the assumption of local adsorption equilibrium with the feed gas al the entrance of the membrane. The model system is a slit-like pore of graphite plane for the membrane and the methane and the ethane for permeating gases. To reach the stationary state in a simulation run, 50,000-60,000 time steps computation and 500-2,000 molecules in a cell are required for obtaining better statistics in the NEMD. Computer graphics animations clearly show that molecules having entered the pore gather together in monolayers on the surface to form downstream surface flow. Under a constant feed pressure condition, the mass fluxes of gases decrease significantly with increasing temperature because of the decrease in pore density in adsorption equilibrium with a feed gas. In the case of binary mixture permeation, enhanced selectivity of more adsorptive substance (ethane) was observed with an decrease in temperature, the reason for which is the significant decrease in pore density of methane, a weaker adsorptive, due to tile competitive adsorption of ethane.