PURPOSE: To produce 2,4-diphenyl-4-methyl-1-pentene from α-methylstylene with high yield and high selectivity by using a dimerization catalyst of α-olefin which consists of such two kinds of metallic oxides as highest acid strength and the mean electronegativity of two kinds of metallic ions show specific value.

CONSTITUTION: In a dimerization catalyst capable of producing 2,4-diphenyl-4- methyl-1-pentene from α-methylstylene in high yield, a dimerization catalyst of α-olefin containing an aromatic hydrocarbon group is used which consists of such two kinds of metallic oxides as highest acid strength is ≤-2 as indication by an acidity function and the mean electronegativity of two kinds of metallic ions is ≥9. Either of a zirconium oxide-silicon oxide and a titanium oxide-aluminum oxide is used as two kinds of metallic oxides. As a ratio of two kinds of metallic oxides, for example, in the case of the binary metallic oxide of titanium and silicon, the ratio of titanium oxide to silica is set up in a range within (50:50) to (85:15).