A process for producing an olefin copolymerization catalyst, comprising the step of contacting, with one another, (A) a solid catalyst component containing a titanium atom, a magnesium atom and a halogen atom, (B) an organoaluminum compound and/or organoaluminumoxy compound, and (C) a nitrogen-containing aromatic heterocyclic compound, whose one or more carbon atoms adjacent to its nitrogen atom are linked to an electron-withdrawing group, or a group containing an electron-withdrawing group; and a process for producing an olefin copolymer using the an olefin copolymerization catalyst.