Natural rubber (NR)/carbon nanotube/ionic liquid nanocomposite membranes, prepared by using sulfur as the crosslinking agent, are tested for their vapor permeation (VP) characteristics. The permeation studies are conducted using three solvents, pentane, hexane and heptane as aliphatic solvents and toluene as aromatic solvent. The effects of the ionic liquid loading, CNT loading, and penetrant size on the vapor permeability of the membranes are investigated. The vapor permeability of the nanocomposite is found to increase with an increase in the ionic liquid content and decreases with CNT loading. Generally, cyclohexane is produced by the catalytical hydrogenation of benzene at high temperature. It is very difficult to purify it by removing unreacted benzene due to the close boiling point of cyclohexane and benzene and their azeotropic mixture formation tendency. By using NR/CNT/IL nanocomposite membrane, VP technique is applied for the separation of benzene/cyclohexane mixtures, including azeotropic composition of the solvents. The gas permeabilities of the NR, NR/CNT3, and NR/CNT3/IL membranes are determined with nitrogen and oxygen. Among these membranes, NR/CNT3/IL shows highest permeability. Compared to nitrogen, oxygen shows higher permeability.