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 cyclohexene-1,2-dicarboxylate, di-n-butyl 1,3-cyclohexadiene-1,2-dicarboxylate, diethyl furane-3,4-dicarboxylate, di-n-butyl 3,4-dihydro-2H-pyrane-5,6-dicarboxylate, diethyl ester of cyclohexene-1,6-dicarboxylic acid, and so on.