Different carbon black composite (CBC) supported molybdenum carbides were synthesized. The support was functionalized with nitric acid at different pH of the impregnation solution (pH 5.2; 0), in order to improve the active phase dispersion. After characterization of these supported catalysts, the kinetic study of the hydrodesulfurization (HDS) of dibenzothiophene (DBT) was for the first time performed over functionalized CBC supported molybdenum carbides. It was found that the HDS of DBT proceeds via the two classical parallel routes: the hydrogenation route (HYD) leading to cyclohexylbenzene and bicyclohexyl and the direct desulfurization route (DDS) leading to biphenyl. In all cases the DDS route was more favored than the HYD route, as well as more inhibited by indole. A global kinetic model suitable for all catalysts is proposed. It could describe all experimental data, and global rate constants were calculated for the HDS of DBT. The corresponding detailed kinetics of the HDS of DBT was also put forward, considering two types of active sites and expressions for the global rate constant could be determined. Furthermore, when the CBC support was preoxidized with HNO3, the dispersion of the molybdenum carbide active phase was improved and a higher HDS activity was observed both in the absence or in the presence of indole.