An anionic polymerizable monomer is added to a reaction system in which an anion species which is incapable of initiating polymerization but may react with polymerization inhibiting substances to convert them into compounds that do not inhibit polymerization is present, and then an anion species capable of initiating polymerization is added thereto. It becomes possible to produce high molecular weight polymers and to precisely control the molecular weight thereof even if polymerization inhibiting substances are present in the system or when polymerization inhibiting substances enter from outside.