A process for the dimerization of lower olefins characterized by the use of a ternary catalyst comprising (1) at least one salt or complex of a platinum-group transition metal of the periodic table, (2) at least one organoaluminum compound and (3) at least one inorganic metal compound. This process enables the dimerization of lower olefins in an extremely high yield at an extremely high selectivity and at an extremely high recovery of catalyst.