A process for preparing a catalyst component supported on a carrier which comprises contacting a titanium tetrahalide in the liquid or gaseous phase with a solid in the absence of mechanical pulverization, said solid being obtained by mechanically pulverizing specified combinations of components selected from the group consisting of a magnesium dihalide component selected from magnesium dihalides and adducts thereof with monocyclic aromatic monocarboxylic acid esters; a monocyclic aromatic monocarboxylic ester; and a titanium component selected from titanium compounds of the formula Ti(OR).sub.n X.sub.4-n wherein R is alkyl or optionally substituted phenyl, X is halogen, and n is an integer of 0 to 4 and complexes thereof with monocyclic aromatic monocarboxylic acid esters, the amounts of the magnesium dihalide (a), the monocyclic aromatic monocarboxylic acid ester (b), and the titanium compound (c) being selected such that the molar ratio of (a):(b):(c) is 1: (not less than 0.005):(100 to 0.001).