The invention relates to a process for the hydrotreatment of an olefinic gasoline comprising at least one selective hydrogenation stage, and generally of simultaneous conversion of mercaptans by weight increase, in which the makeup hydrogen used in this stage or these stages has a reduced CO+CO.sub.2 content, preferably comprised between 5 and 200 ppmv. Most often, the CO content is comprised between 1 and 20 ppmv. The process typically makes it possible to hydrorefine an olefinic gasoline by more or less eliminating the diolefins and sulphur compounds.