A catalyst for polymerization of an olefin, said catalyst being formed from[A] a solid titanium catalyst component comprising magnesium, titanium, halogen and an electron donor as essential ingredients,[B] an organoaluminum compound catalyst component, and[C] an electron donor catalyst component comprising at least two electron donors including an electron donor (1) and an electron donor (2), the MFR (a) of homopolypropylene obtained by using the electron donor (1) together with the solid titanium catalyst component [A] and the organoaluminum compound catalyst component [B] has the following relation to the MFR (b) of homopolypropylene obtained by using the electron donor (2) under the same polymerization conditions as in the case of using the electron donor (1)log [MFR (b)/MFR (a)].gtoreq.1.5.This catalyst can give an olefin polymer having a broad molecular weight. Also provided is a process for polymerizing or copolymerizing an olefin in the presence of the above catalyst.