A method for manufacturing a polymer by performing an anionic polymerization reaction by a flow-type reaction, including: 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; subjecting the anionic polymerizable monomer to anionic polymerization while a solution formed by the joining is flowing to downstream in the reaction flow path; and causing a polymerization reaction solution flowing in a reaction flow path and the polymerization terminator to join together such that the polymerization reaction is terminated; and a flow-type reaction system suitable for performing the manufacturing method.