Abstract: A process for producing an olefin oligomer by the polymerization of an olefin in the presence of boron trifluoride as a catalyst, and further in the co-presence of water and/or an alcohol and a carboxylic acid anhydride as a co-catalyst. The process has advantages that (i) olefin oligomers having a low viscosity can be produced at high yields, (ii) the production efficiency can be improved by decreasing the time required for the reaction, (iii) the amount of the co-catalyst required can be decreased, and (iv) the viscosity of an olefin oligomer to be obtained can be freely controlled by changing the amounts of the olefin, the catalyst, the co-catalyst, etc.