PURPOSE: To rapidly polymerize titled polymer useful as a papaer-strengthening agent, a polymer coagulating agent or the like, by purifying, by means of an ion exchange resin, an aqueous solution of crude acrylamide obtained by catalytically hydrating acrylonitrile in the presence of a copper-containing catalyst.

CONSTITUTION: An aqueous solution of crude acrylamide obtained by catalytically hydrating acrylonitrile in the presence of metallic copper or a metallic copper-containing catalyst, is passed sequentially through an H-type cation exchange resin layer, a weak acid salt type strong base anion exchange resin layer and an H-type weak acid cation exchange resin layer. Next, the treated solution is polymerized to produce an acrylamide dolymer. When the aqueous acrylamide solution subjected to the specified ion exchange resin treatment is used as a meterial, the rate of polymerization of the monomer becomes higher as compared with a case when acrylamide purified by recrystallization is used as a raw material. This difference in polymerization rate is distinct in case where a low-polymerization rate formulation is used.