A catalyst component obtained by a process comprising contacting (a), (b) and (c) described below, a catalyst for addition polymerization using the catalyst component, and a process for producing an addition polymer with the catalyst for addition polymerization: (a) a compound represented by the chemical formula, BiL.sup.1.sub.r, (b) a compound represented by the chemical formula, R.sup.1.sub.s-1T.sup.1H, and (c) a compound represented by the chemical formula, R.sup.2.sub.t-2T.sup.2H.sub.2, wherein r is a numeral corresponding to a valence of Bi; L.sup.1 is a hydrogen atom, a halogen atom, a hydrocarbon group or a hydrocarbon oxy group; T.sup.1 and T.sup.2 independently represents a non-metallic atom of Group 15 or 16 of the periodic table; s represents a numeral corresponding to a valence of T.sup.1; t represents a numeral corresponding to a valence of T.sup.2; R.sup.1 is an electron-withdrawing group or an electron-withdrawing group-containing group; and R.sup.2 represents a hydrocarbon group.