FIELD: olefin polymerization and polymerization catalysts. SUBSTANCE: catalyst component for polymerization of olefins with general formula CH2=CHR, where R is hydrogen or C1-C10-alkyl, containing magnesium halide as carrier and active component which is product of interaction of (i) titanium compound containing at least one Ti-OR' linkage where R' is lower alkyl and (ii) solid product obtained from cleavage (leading to formation of magnesium halide and magnesium halide-containing product) of complex with general formula MgX2•nAlR″X1
2p
AlX
3 (A) where X is chlorine and bromine; X' chlorine, bromine, or alkoxy group; R" C
1-C
20-alkyl; n=1-6; p varies from 0 to 1; and n+p=1-6. Catalyst component is distinguished by being spherically shaped and having porosity (measured by mercury technique) higher than 0.5 qu.cm/g. Method of its preparation consists in that spherical carrier is impregnated with hydrocarbon solution of titanium compound "i" and then is brought into reaction with complex A. Another olefin-polymerization catalyst consists of above-described component and an alkyl-aluminum compound. When catalyst is used in gas-phase polymerization of ethylene or with its mixture with other alpha- olefins, polymers are obtained with relatively narrow molecular weight distribution and with uniform distribution of comonomers in polymer chain. EFFECT: increased selectivity of catalyst. 18 cl