PURPOSE: To obtain a transition metallic compound, represented by a specific formula, suitable as a principal component of a highly active catalyst for polymerizing an olefin, reduced in production cost and capable of efficiently producing the catalyst at a low cost.

CONSTITUTION: The compound of the formula [M denotes a group III to X or a lanthanoid series metallic element of the periodic table; X denotes a σ- binding ligand capable of binding to M; Y denotes a Lewis base, etc.; A denotes a cross-linking atom; (p) denotes 1-20; (q) denotes 1-5 and [(valence of M) -2]; (r) denotes 0-3; R1 to R6 denote each H, a halogen, a 1-20C hydrocarbon, a hydrocarbon containing a halogen, a group containing silicon or a group containing a hetero-atom], e.g. 1,2-ethanediyl(1-indenyl) (2-indenyl)zirconium dichloride. Furthermore, the objective compound is preferably obtained by reacting, e.g. the corresponding substituted cycloalkenyl anion with a halide of the M.