Hierarchical composite catalysts were made with Zn ion-exchanged ZSM-5 and mesoporous alumina using conventional kneading method. Cracking and dehydrocyclization of n-hexane was performed using a fixed bed reactor in order to investigate the effects of the matrix on the catalytic activity and the product selectivity. Cracking of n-hexane and successive dehydrocyclization of formed olefins to produce aromatics proceeded at H2 atmosphere and temperature 450–550 °C. The conversion of n-hexane and the aromatics selectivity enhanced with raising temperature and tended to increase with increasing the amounts of acid sites. When 10 wt% of alumina was used among catalysts with similar Zn content, the selectivity for aromatics reached maximum of about 42–45%, indicating that the optimal amount of alumina would exist to obtain the high selectivity and that the amount of ZnZSM-5 would be enough large to enhance aromatic compounds to the maximum. Reaction routes for aromatization of n-hexane could be proposed by assuming three routes of the initial cracking of n-hexane to C1 and C5, C2 and C4 and two molecules of C3, the successive cracking of the formed C5, and the final aromatization forming benzene, toluene and xylenes through Diels–Alder reactions of C2–C6 olefins.