In the present invention, at least a monomer and a chain transfer agent are fed to a reactor and the time when the temperature of the solution inside the reactor reaches a pre-determined polymerization temperature is set as the start time T0, while the time when the operation to stop the polymerization reaction is started is set as the end time T1. A polymerization initiator is fed to inside the reactor sometime between T0 and immediately before [(T1-T0)/2] and sometime between [(T1-T0)/2] and T1. The total mass of polymerization initiator fed between T0 and T1 is IA and the total mass of polymerization initiator fed between [(T1-T0)/2] and T1 is IB. IA is 50 to 100 mass% of the total amount of polymerization initiator, and a polymer wherein the chain transfer residues remaining at the polymer termini are reduced and fluctuations in molecular weight are improved can be produced with a high degree of conversion by a production method that satisfies 0.50 B/IA<1.00.