The method for producing a polymer produces a polymer which has at least two peaks in the molecular weight distribution curve of the polymer as obtained by molecular weight measurement by means of GPC, and which is a conjugated diene polymer or a copolymer of an aromatic vinyl compound and a diene compound. The method for producing a polymer uses a reaction apparatus wherein two or more reactors for continuous polymerization are connected in series with each other. A polymerization reaction is carried out by introducing a monomer component and a polymerization initiator into the first reactor;and subsequently, polymerization is carried out by adding a monomer component and a polymerization initiator just before each of the second and subsequent reactors. The weight average molecular weight of a polymer (A) obtained in the first reactor is from 300000 to 2000000.