A process for producing a polymer or copolymer of an olefin which comprises polymerizing or copolymerizing at least one olefin with or without a diolefin in the presence of a catalyst composed of (A) a magnesium-containing solid titanium catalyst component containing magnesium, titanium, a halogen and an electron donor as essential ingredients and (B) an organoaluminum compound catalyst component; characterized in that(1) said catalyst further comprises (C) an organic silicon compound catalyst component having an Si--O--C or Si--N--C bond, and(2) said electron donor in the catalyst component (A) is a cyclic mono- or poly-ester such as diethyl furane-3,4-dicarboxylate, di-n-butyl 3,4-dihydro-2H-pyrane-5,6-dicarboxylate, di-isobutyl pyrrole-2,3-dicarboxylic, di-n-butyl thiophene-2,3-dicarboxylate, n-octyl pyrrolidine-2,3-dicarboxylate, and so on.