A catalyst for polymerization of olefins or styrenes, which is prepared by contacting (A) a transition metal compound, (B) at least one material selected from the group consisting of oxygen-containing compounds and compounds which react with a transition metal compound to form an ionic complex, and optionally (C) an alkylating agent with each other, and contacting these materials (A), (B) and (C) with an adsorbing substance (D), during or after the contact of materials (A), (B) and (C) with each other, followed by removing the adsorbing substance (D) from the contacted materials (A), (B) and (C).