A method of removing a residual catalyst metal compound from a polymer solution comprises the steps of: a) mixing a solution in which at least one organic nitrogen compound is dissolved in a polar solvent and the polymer solution to precipitate a chelate compound of the organic nitrogen compounds and the residual catalyst metal compound, b) adding the polar solvent to the solution mixture to dissolve a chelate compound and to precipitate a polymer, and c) filtering the precipitated polymer. After the polymer polymerization is completed, an organic nitrogen compound solution is added to perform a chelate reaction with the residual catalyst metal compound in a solution phase, and the polar solvent is added to precipitate the polymer so that only polymer precipitates are filtered while an additional filtration process in respect to the chelate compound is not performed to easily remove the residual catalyst metal compound.