Ziegler polymerization of C.sub.3 or higher .alpha.-olefins is disclosed which is characterized by a solid catalyst component and an organoaluminum component used in the Ziegler catalyst, and also by the temperature used which is 150.degree. to 300.degree. C. The solid catalyst component, Component (A), comprises Sub-component (i) which is a solid catalyst component for Ziegler catalysts comprising Ti, Mg and a halogen; Sub-component (ii) which is a silicon compound represented by a formula: R.sup.1.sub.m X.sub.n Si(OR.sup.2).sub.4-n-m wherein R.sup.1 indicates a hydrocarbyl group, R.sup.2 which may be the same as or different from R.sup.1 indicates a hydrocarbyl group, X is a halogen atom, and m and n are each a number satisfying equations 0.ltoreq.m.ltoreq.3, 0.ltoreq.n.ltoreq.3 and 0.ltoreq.m+n.ltoreq.3; and Sub-component (iii) which is an organometal compound of a metal of Groups I to IV of the Periodic Table. The organoaluminum component (B) is an organoaluminum compound represented by a formulaR.sup.3.sub.3-p H.sub.p Alwherein R.sup.3 indicates a hydrocarbyl group of up to 5 carbon atoms and p is a number satisfying an equation 0.ltoreq.p.ltoreq.1;the mole ratio in Al/Ti of Component (B) to Component (A) being no higher than 1. The poly .alpha.-olefins produced have a broader molecular weight distribution than those produced at a lower polymerization temperature.