PURPOSE: To obtain a catalyst composition capable of efficiently providing a polymer good in distribution of composition, film appearance and particle properties with a high activity by coating a particulate inorganic oxide having a specified particle diameter with a solution containing a specific transition metallic compound and a Lewis acid, etc., in a hydrocarbon.

CONSTITUTION: This catalyst composition is obtained by coating (A) a particulate inorganic compound consisting essentially of an inorganic oxide having 0.003-1μm average particle diameter (e.g. silica) with (B) a homogeneous or a heterogeneous solution containing (i) a compound of a group IVB transition metal of the Periodic Table [e.g. bis(dicyclopentadienyl)zirconium monochloride hydride] and (ii) at least either of a Lewis acid (e.g. aluminum chloride) and an ionic compound, reactive with the component (i) and capable of converting the component (i) into a cation (e.g. tetraphenylboron) in a hydrocarbon (e.g. toluene). The wt.% ratio (A:B) of the components (A) and (B) is (5-50):(95-50) and the catalyst composition is capable of efficiently producing an olefin polymer excellent in quality thereof.