A process for producing polyolefins having a high stereoregularity, no smell and a good particulate form, without needing removal of catalyst residue contained in the resulting polyolefins, which process comprises polymerizing olefins by the use of a catalyst obtained by combining a solid product (II) as a solid catalyst component prepared through the following reaction steps I, II and III, with an organoaluminum compound component and an organic silicon compound component having Si-O-C bond: Step I of mixing and dissolving .circle.a an anhydrous Mg dihalide, .circle.b a specified orthotitanic acid ester or/and a specified polytitanic acid ester and .circle.c a saturated or unsaturated, mono- or polyhydroxy alcohol of 1.about.20 C in an inert hydrocarbon solvent to obtain a component (A), Step II of mixing (A) with a component (B) consisting of .circle.d an aliphatic or aromatic monocarboxylic acid ester, .circle.e a specified halogenated aluminum and .circle.f a specified halogenated silicon to obtain a solid product (I), and Step III of reacting (I) with a component (C) consisting of .circle.g a specified halogenated titanium or/and .circle.h a specified halogenated vanadyl or a specified vanadium halide to obtain the solid product (II).