The present invention provides a catalyst component for polymerization of olefin CH.sub.2.dbd.CHR, in which R is hydrogen or C.sub.1-C.sub.12 alkyl or aryl, comprising magnesium, titanium, a halogen and an electron donor compound (a) which is at least one selected from the group consisting of dibasic ester compounds of the formula (I), and said catalyst component optionally further comprising an electron donor compound (b) selected from the group consisting of aliphatic dicarboxylic esters and aromatic dicarboxylic esters, and/or an electron donor compound (c) selected from the group consisting of 1,3-diether compounds of formula (IV): ##STR00001## wherein, R.sub.1, R' and A are as defined in the description, ##STR00002## wherein R.sup.I-R.sup.VIII are as defined in the description, and a catalyst comprising the catalyst component.