A process is described for the upgrading of hydrocarbon mixtures which boil within the naphtha range containing sulfur impurities, i.e. a hydrodesulfuration process with contemporaneous skeleton isomerization and reduced hydrogenation degree of the olefins contained in said hydrocarbon mixtures, the whole process being carried out in a single step. The process is carried out in the presence of a catalytic system comprising a metal of group VI B, a metal of group VIII and a carrier of acid nature consisting of a mesoporous silico-alumina.