Separation of benzene and cyclohexane by a NaY zeolite membrane was studied via grand canonical molecular dynamics (GCMD). The GCMD technique was recently developed by simulation methods and effective for the study of the membrane separation process at the molecular level since it can simulate the dynamics of the permeants at a constant pressure gradient. From the simulation results of benzene single-component permeation, benzene molecules were preferably located at the C site in a NaY membrane. Distribution of benzene molecules around sodium ions on the SII site in a binary mixture system was almost the same as that of the single component, whereas the distribution of cyclohexane molecules around SII sodium ions in a single-component and binary mixture system was different. Calculated permeation flux of cyclohexane showed a higher value than that of benzene in a single component. On the other hand, in the binary mixture system, the cyclohexane flux was reduced significantly compared to the single-component one. A derived separation factor was completely reversed for the single-component and binary systems. This tendency is the same as observed in experiments.