Polyolefins exhibiting better particle properties are prepared by polymerizing an olefin or olefins in the presence of a catalyst comprising a solid catalyst component and an organometallic compound, said solid catalyst component being prepared by the reaction of the following components [I] and [II] :
[I] a reaction product obtained by reacting the following components (1), (2) and (3) with one another in the presence of a compound represented by the general formula ROH wherein R is a hydrocarbon radical having 1 to 20 carbon atoms or an organic residue containing such an element as oxygen, nitrogen, sulfur, or chlorine:
(1) a silicon oxide and/or an aluminum oxide; (2) a reaction product obtained by the reaction of a magnesium halide and compound represented by the general formula Me(OR) n X z - n wherein Me represents an element of Groups I to IV in the Periodic Table, z represents the valence of the element Me, n is 0 (3) a titanium compound represented by the general formula Ti(OR) n X 4 - n wherein R is a hydrocarbon radical having 1 to 20 carbon atoms, X is a halogen atom, and n is 0 ≦ n ≦ 4; and [II] an organoaluminum compound represented by the general formula Al(OR′) m R² n X 3 - (m + n) wherein R¹ and R² are each a hydrocarbon radical having 1 to 24 carbon atoms, X is hydrogen atom or a halogen atom, and m and n are 0