PURPOSE: To obtain a highy stereoregular polymer in high yield by the polymerization of an α-olefin using a catalyst comprising three components, namely, organoaluminum compound, electron donor and a solid of specific surface area prepared by bringing specific Mg compound into contact with halogen-contg. compound and oxygen-contg. Ti compound followed by treatment with TiCl4.

CONSTITUTION: The objective steroregular polymer can be obtained by the polymerization of an α-olefin using a catalyst comprising the following three components: (A) an amorphous solid product of a specific surface area <40m2/g prepared by carrying out a reaction through bringing, in the presence or absence of organic ester, (i) a Mg compound of formula I (R1 is 1W10C alkyl, allyl, etc.; X1 is halogen, n is 1.0W2.0) into contact with (ii) halogen-contg. compounds such as halogenated hydrocarbon, oxygen-contg. halogenated hydrocarbon, halogenated thionyl, halognated phosphorus compound and halogen-contg. nitrogen compound and (iii) an oxygen-contg. Ti compound of formula II (R2 is HOC alkyl, allyl, etc.) followed by treatment once, twice or more with TiCl4, (B) an organoaluminum compound, and (C) an electron donor.