Hydrodesulfurization of dibenzothiophene (DBT) by an unpromoted acidic zeolite has been theoretically studied using density functional theory method with the cluster approach. Different reactions have been investigated. The direct hydrodesulfurization of DBT and the hydrodesulfurization of hydrogenated DBT are described. Furthermore, aromatic hydrogenation has been considered. A detailed description of the intermediates and transition states corresponding to the different reaction pathways is provided. The elementary DBT cracking reaction, which leads to the formation of biphenylthiol, is the most difficult reaction in the DBT hydrodesulfurization reaction pathway. Once this step has been achieved, sulfur removal becomes favorable. However, aromatic hydrogenation appears to be a more favorable reaction than DBT cracking. It is predicted that hydrogenation will preferentially take place. The ring cracking activation energies of hydrogenated DBT are on the same order as those of aromatic hydrogenation.