The invention relates to a process for converting a hydrocarbon charge of linear and branched olefins, comprises the following stages: a) a stage of membrane separation of the hydrocarbon charge under conditions making it possible to produce a cut β containing the majority of the linear olefins present in said charge, and a cut γ containing the majority of the branched olefins, b) a stage of treatment of the linear olefins contained in the effluents originating from the membrane separation stage (cut β) under moderate oligomerization conditions, c) a stage of distillation separation of the effluents originating from the oligomerization stage into at least two cuts, d) a stage of hydrogenation of the cut η under conditions for obtaining a gas oil with a high cetane number.