PURPOSE: To produce an odorless polyolefin having high stereo-regularity, by polymerizing an α-olefin with a catalyst produced by combining a cyclic phosphazene component with a TiCl3 catalyst component and an organic Al component.

CONSTITUTION: An α-olefin is polymerized preferably in gaseous phase in the presence of a catalyst produced by combining (A) a TiCl3 catalyst component (e.g. a compound produced by reducing TiCl4 with an organic Al compound and treating the resultant TiCl3 with an electron donative compound and TiCl4), (B) an organic Al compound (e.g. triethylaluminum, ethylaluminum dichloride, etc.) and (C) a cylclic phosphazene component (e.g. hexakisethylthiocyclotriphosphazene). The amount of the component B is usually 1W500 mol per 1 mol of Ti atom in the component A and that of the component C is 0.01W1 mol per 1 mol of the component B.