The present invention relates to a solid complex titanium catalyst for
homo-polymerization and co-polymerization of .alpha.-olefin, obtained by
(i) producing a solution of a magnesium compound by dissolving a magnesium
compound and a compound of IIIA Group of the Periodic Table in a solvent
mixed with cyclic ether, one or more types of alcohol, a phosphorous
compound, and an organosilane, (ii) precipitating the solid particles by
reacting said magnesium solution with a compound of a transition metal, a
silicon compound, or the mixture thereof, and (iii) reacting said
precipitated solid particles with a titanium compound and an electron
donor. The catalyst of the present invention is of large particle size,
narrow particle distribution, and high catalytic activity, while the
polymers obtained with the use of this catalyst are of excellent
stereoregularity.