This invention provides method of producing a polymer which comprises substitution of carboxylic acid group for a terminal halogen group of a polymer obtainable by atom transfer radical polymerization. The carboxylic acid group may be a carboxylic acid salt group, more preferably a carboxylic acid potassium salt group. In carrying out the atom transfer radical polymerization in the practice of the invention, a transition metal complex can be used as a polymerization catalyst. The transition metal complex may be a transition metal complex with an element of the group 7, 8, 9, 10 or 11 of the periodic table as the central atom, more preferably a copper, nickel, ruthenium or iron complex and, in particular, a copper complex is used. The polymer obtainable by atom transfer radical polymerization is obtained by polymerization of a (meth)acrylic monomer, particularly the polymer obtained by polymerization of an acrylic acid ester monomer.