Water-soluble high molecular weight polymers, useful as coagulating agents, are prepared by initiating the polymerization of acrylamide or a monovinyl monomer mixture containing a predominant amount of acrylamide in an acetone-water mixture at a temperature of not lower than 5.degree.C but of lower than 25.degree.C in the presence of polyvinyl alcohol and a catalyst, the concentration of the monomer in the polymerization reaction mixture being 15 to 30 % by weight and the concentration of acetone in the acetone-water mixture being 15 to 35 % by weight, and continuing the polymerization reaction while controlling the viscosity of the reaction system by adding a water-miscible organic solvent having a small chain transfer coefficient to the reaction system with the progress of the polymerization reaction.