A process for homopolymerizing an olefin or copolymerizing an olefin with another olefin in the presence of a catalyst composed of(a) a solid catalyst component containing magnesium atoms, titanium atoms, halogen atoms, and an electron donor compound,(b) an organoaluminum compound represented by the formula R.sup.1 R.sup.2 R.sup.3 Al (wherein R.sup.1, R.sup.2, and R.sup.3, which may be the same or different, each denote a C.sub.1-20 alkyl, alkenyl, cycloalkyl, aryl, aralkyl, or alkoxy group, or a hydrogen atom;(c) an organoaluminum compound represented by the formula R.sup.4.sub.3-n AlX.sub.n (wherein R.sup.4 denotes a C.sub.1-20 alkyl, alkenyl, cycloalkyl, aryl, aralkyl, or alkoxy group; X denotes a halogen atom; and n.gtoreq.1),(d) an electron donor compound containing a nitrogen atom, sulfur atom, oxygen atom, or phosphorus atom, and(e) an aromatic ester compound.