In anionic polymerization using an anionic polymerization initiator, a tertiary organoaluminum compound (A) having in the molecule thereof a chemical structure represented by a general formula: Al—O—Ar wherein Ar represents an aromatic ring, and at least one Lewis base (B) selected from the group consisting of an ether compound and a tertiary polyamine compound are caused to be present in the polymerization system. In this way, the polar monomer can be polymerized with a high polymerization initiation efficiency and a high living polymerization property and at a high polymerization rate even if the used polymerization initiator is suitable for industrial use and a relatively mild cooling condition or a temperature condition near room temperature is adopted as a polymerization temperature condition.