(1) A methacrylic ester or an acrylic ester is anionically polymerized, using a polymerization initiator compound comprising an addition reaction product of a conjugated diene compound and an organic alkali metal compound, in the presence of a tertiary organoaluminum compound having in the molecule thereof a chemical structure represented by a formula: Al—O—Ar wherein Ar represents an aromatic ring; or (2) a methacrylic ester or an acrylic ester is anionically polymerized, using a polymerization initiator compound comprising an addition reaction product of an organic alkali metal compound and a compound having a 1,1-diaryl-1-alkene structure, by adding the ester in the form of a mixture with the above-mentioned specific tertiary organoaluminum compound to the polymerization system. In this way, various species of the esters can be anionically polymerized with a high initiation efficiency and a high living polymerization property in a solvent which can easily be recovered and reused under a mild cooling condition, using an organic alkali metal compound which has relatively good convenience.