A method for producing a polymer selected from an ABA block copolymer, a star polymer, a bottle brush polymer, a dense polymer brush, and a heterogeneous graft/block/multi-branched polymer, the method comprising a polymerization step of mixing and warming at least: a radically polymerizable monomer having an unsaturated bond; an organic compound wherein at least two groups that function as a group for initiating polymerization of the monomer and that have a structure represented by the following formula 1 or the following formula 2 which is introduced in a molecule of the organic compound; and an iodine ion-containing compound being at least one iodide salt or triiodide salt selected from the group consisting of metal iodides, quaternary ammonium iodides, quaternary phosphonium iodides, and quaternary ammonium triiodides, thereby initiating, from the group having the structure, radical polymerization accompanied by a termination reaction without using a metal-based catalyst for use in the living radical polymerization: wherein, R 1 represents H or an arbitrary alkyl or acyl group, R 2 represents an arbitrary alkyl or aryl group, X represents Cl or Br, and Y represents O or NH; or wherein the group of Formula 1 is a group according to one of the following formulae:; and wherein R 3 represents H or an arbitrary alkyl or aryl group, R 4 represents an aryl group, a cyano group, a carboxyl group, an ester group, or an amide group, and X represents Cl or Br, wherein at least any one selected from the group consisting of iodine; an N-iodoimide-based compound as an iodinated organic compounds capable of releasing iodine; and compounds each having an organic base is further used in the polymerization step, wherein any of azo-based radical polymerization initiators, peroxide-based radical polymerization initiators, and photo-radical polymerization initiators is not used in the polymerization step. a radically polymerizable monomer having an unsaturated bond; an organic compound wherein at least two groups that function as a group for initiating polymerization of the monomer and that have a structure represented by the following formula 1 or the following formula 2 which is introduced in a molecule of the organic compound; and an iodine ion-containing compound being at least one iodide salt or triiodide salt selected from the group consisting of metal iodides, quaternary ammonium iodides, quaternary phosphonium iodides, and quaternary ammonium triiodides, wherein, R 1 represents H or an arbitrary alkyl or acyl group, R 2 represents an arbitrary alkyl or aryl group, X represents Cl or Br, and Y represents O or NH; or wherein the group of Formula 1 is a group according to one of the following formulae:; and wherein R 3 represents H or an arbitrary alkyl or aryl group, R 4 represents an aryl group, a cyano group, a carboxyl group, an ester group, or an amide group, and X represents Cl or Br, wherein at least any one selected from the group consisting of iodine; an N-iodoimide-based compound as an iodinated organic compounds capable of releasing iodine; and compounds each having an organic base is further used in the polymerization step, wherein any of azo-based radical polymerization initiators, peroxide-based radical polymerization initiators, and photo-radical polymerization initiators is not used in the polymerization step.