An inert hydrocarbon catalyst is a mixture of 1 mol of (A) a reaction product obtained by reacting in an inert hydrocarbon solvent (a) 1 mol of at least one V compound VO(OR) m X 3-m wherein R is a hydrocarbon group, X a halogen atom and m a real number of from 0 to 3 (preferably 0), and (b) 0.5 to 1.4 mols of a dihydroxy hydrocarbon compound constituted of a C2-12 straight chain hydrocarbon skeleton having a hydroxyl group at each end terminal and at least one hydrocarbon branch bonded to said hydrocarbon skeleton, and 2 to 500 mols of (B) at least one organoaluminum compound represented by R′ n AℓX′ 3-n wherein R′ is a hydrocarbon group, X′ a halogen atom; and n a real number more than 0 and less than 3. The catalyst is dissolved in an aliphatic or alicyclic hydrocarbon solvent (e.g. hexane) to which is added an olefin (e.g. α-olefin alone or with ethylene and/or a polyene), to polymerise, at 0- 100°C under pressure of 5-50 kg/cm² to produce olefinic hydrocarbon polymers having narrow distributions of molecular weight and composition with high efficiency and high polymerization activity, without obstruction or contamination of equipment due to precipitation of catalyst.