Method for polymerizing .alpha.-olefin

A method for polymerizing an .alpha.-olefin which comprises bringing, in the presence of an organic acid ester, a feed containing at least one .alpha.-olefin having 3 or more carbon atoms into contact with a catalyst comprising (A) a solid catalytic ingredient which has been prepared in such a manner that (a) a Grignard compound of the formula (I):

• R.sup.3 M.sub.g X (I)
• wherein R.sup.3 represents an alkyl radical having 1 to 8 carbon atoms and X represents a halogen atom, is reacted with a reaction product of an aluminium halide with an organic silicon compound of the formula (II):
• R.sub.n.sup.1 Si(OR.sup.2).sub.4-n (II)
• wherein R.sup.1 represents a member selected from the group consisting of alkyl radicals having 1 to 8 carbon atoms and a phenyl radical, R.sup.2 represents an alkyl radical having 1 to 8 carbon atoms and n represents an integer of 1, 2 or 3, (b) the resultant solid reaction product is brought into a first contact with a titanium tetrahalide, (c) the resultant titanium-containing solid product is treated with an organic acid ester and, finally, (d) the treated solid product is brought into a second contact with a titanium tetrahalide;
• and (B) another catalytic ingredient consisting of at least one trialkyl aluminium of the formula (III):
• AlR.sub.3.sup.4 (III)
• wherein R.sup.4 represents alkyl radical having 2 to 6 carbon atoms.