To provide a method for producing α-olefin polymer useful for a component of lubricating oil.

The method comprises the polymerization of α-olefin having ≥4 carbons in the presence of (A) a transition metal compound represented by formula (I) (wherein R1 to R12 and X1 to X4 are each independently hydrogen atom, a halogen atom or the like; Y1 to Y4 are each independently a divalent group bounding two ligands, a hydrocarbon group having 1-20C, a hydrocarbon group having 1-20C and halogen and a group containing silicon or the like; M1 and M2 are each a transition metal of groups 4-6 of the Periodic Table) and (B) a catalyst for producing olefin polymer which contains (b-1) an organoaluminum oxy compound and (b-2) one sort selected from ionic compounds.