PURPOSE: To prepare the title catalyst component without requiring removing steps of catalyst residues and atactic polymer, by treating a solid composition, which is obtained through uniting of a magnesium compound with an alkoxytitanium and an acid halide compounds, with an inert solvent.

CONSTITUTION: A magnesium compound, e.g. an Mg halide, alkoxylate, pheroxylate, or an organic carboxylic acid salt, or their mixture is suitably pulverized and united with an alkoxytitanium compound and an acid halide to give a solid composition, which is treated with an inert organic solvent, e.g. aliphatic, alicyclic, aromatic hydrocarbon or their halogenated one. The composition thus obtained as a Ziegler type transition metal component is used for an α-olefin polymerization catalyst in combination with an organoaluminum compound.