An olefin oligomer having a low viscosity and a high viscosity index can be prepared by polymerizing an olefin having 6 or more carbon atoms in the presence of a mixture of a polyhydric alcohol derivative and an aluminum halide, said derivative being obtained by replacing the hydrogen atoms of all the hydroxyl groups of the polyhydric alcohol by either acyl groups exclusively or by acyl group and alkyl groups both of said groups having 1 - 20 carbon atoms. The thus prepared olefin oligomer scarcely contains halogen, and it has a wide range of uses such as, for instance, a lubricant, a cosmetic base, etc.