A method for manufacturing a polymer by performing an anionic polymerization reaction by a flow-type reaction, comprising: introducing a liquid A containing an anionic polymerizable monomer, a liquid B containing an anionic polymerization initiator, and a polymerization terminator into different flow paths respectively and causing the liquids to flow in the respective flow paths; causing the liquid A and the liquid B to join together by using a multilayered cylindrical mixer, wherein the multilayered cylindrical mixer comprises a smallest cylinder (T1) and an adjacent cylinder (T2) which is adjacent to the smallest cylinder, wherein the interior of the smallest cylinder (T1) defines an internal flow path and the portion between the smallest cylinder (T1) and the adjacent cylinder (T2) defines an adjacent flow path; subjecting the anionic polymerizable monomer to anionic polymerization while a solution formed by the joining is flowing to downstream in a reaction flow path; and causing the solution, which has undergone the polymerization reaction and flows in the reaction flow path, and the polymerization terminator to join together such that the polymerization reaction is terminated, characterized in that the liquid flowing in the internal flow path has a linear velocity r1 and the liquid flowing in the adjacent flow path has a linear velocity r2, wherein the ratio of r1 and r2 satisfies the following Expression (I) or (II): r 2 / r 1 ≤ 0.67 r2 / r1 ≥ 1.5 wherein the linear velocity (cm/min) is calculated by dividing a flow velocity (cm 3 /min) of the liquid A or B by a cross-sectional area (cm 2 ) of the respective flow path in the multilayered cylindrical mixer. introducing a liquid A containing an anionic polymerizable monomer, a liquid B containing an anionic polymerization initiator, and a polymerization terminator into different flow paths respectively and causing the liquids to flow in the respective flow paths; causing the liquid A and the liquid B to join together by using a multilayered cylindrical mixer, wherein the multilayered cylindrical mixer comprises a smallest cylinder (T1) and an adjacent cylinder (T2) which is adjacent to the smallest cylinder, wherein the interior of the smallest cylinder (T1) defines an internal flow path and the portion between the smallest cylinder (T1) and the adjacent cylinder (T2) defines an adjacent flow path; subjecting the anionic polymerizable monomer to anionic polymerization while a solution formed by the joining is flowing to downstream in a reaction flow path; and causing the solution, which has undergone the polymerization reaction and flows in the reaction flow path, and the polymerization terminator to join together such that the polymerization reaction is terminated, characterized in that the liquid flowing in the internal flow path has a linear velocity r1 and the liquid flowing in the adjacent flow path has a linear velocity r2, wherein the ratio of r1 and r2 satisfies the following Expression (I) or (II): r 2 / r 1 ≤ 0.67 r2 / r1 ≥ 1.5 wherein the linear velocity (cm/min) is calculated by dividing a flow velocity (cm 3 /min) of the liquid A or B by a cross-sectional area (cm 2 ) of the respective flow path in the multilayered cylindrical mixer. <EOS>