A catalyst for the polymerization of olefins which comprises:(1) a solid catalyst component,(2) a piperidine derivative and(3) an organoaluminum compound,characterized in that the solid catalyst component (A) has been prepared by mixing (a) a dialkoxymagnesium and (b) a diester of an aromatic dicarboxylic acid with (c) a halogenated hydrocarbon to form a suspension and thereafter adding the suspension to (d) a titanium tetrahalide to effect reaction, as well as the solid catalyst component and a process for preparing same. The catalyst maintains a high polymerization activity combined with stereospecific performance over a prolonged polymerization time and scarcely incurs any problem of corrosion and odor in the resultant polymer.