Abstract: Titanium trichloride catalytic component and homo- or co-polymerization of .alpha.-olefin by employing the titanium trichloride catalytic component combined with organic aluminium compound, wherein the titanium trichloride catalytic component is prepared by a process comprising the following steps:first step: reducing titanium tetrachloride with an organoaluminum compoundsecond step: treating the resultant reduced solid, which is obtained by the first step, with an organic ether compoundthird step: reacting the treated solid, which is obtained by the second step, with titanium tetrachlorideand whose objects lie in producing polymer of high stereo-regularity advantageously by carrying out reaction of the first step in a single solvent of aromatic compound or a mixed solvent of aliphatic hydrocarbon and aromatic compound.