A process for producing an olefin oligomer, which comprises the steps of (1) contacting an olefin with an organoaluminum compound to produce a contact product (i), (2) contacting a transition metal compound with a compound represented by the formula, R1R2A-G-AR3R4, to produce a contact product (ii), and (3) contacting the contact product (i), the contact product (ii), an alumoxane compound, and optionally an olefin with one another, wherein A is a nitrogen atom, a phosphorus atom, an arsenic atom or an antimony atom, and As are the same as or different from each other; G is a divalent group; and R1, R2, R3 and R4 are independently of one another a hydrocarbyl group, a halogenated hydrocarbyl group, an oxygen-containing hydrocarbyl group, a sulfur-containing hydrocarbyl group, a selenium-containing hydrocarbyl group, or a tellurium-containing hydrocarbyl group.