A process for oligomerizing an olefinic hydrocarbon feed is described which consists of bringing said feed into contact with a catalyst comprising a silica-alumina, the silica content of said catalyst being in the range 5% to 95% by weight, said catalyst being prepared using a process comprising at least: a) mixing at least one alumina compound which is partially soluble in an acid medium with either at least one silica compound which is completely soluble in the reaction mixture or a combination formed by at least one silica compound and at least one alumina compound, said silica and alumina compounds being completely soluble in the reaction mixture, in order to form a solid precursor of said catalyst; b) hydrothermal treatment of the solid derived from step a) by calcining in moist air for a period in the range 4 to 7 hours.