Provided is a method of producing high-purity nickel sulfate by an impurity-element removal method for selectively removing Mg from a Ni-containing solution. The method comprises a production process of producing nickel sulfate from a Ni-containing acid solution, the acid solution being treated in order of steps (1) to (3): (1) carbonation step, adding a carbonating agent into the Ni-containing solution to make Ni contained in the Ni-containing solution into a precipitate of nickel carbonate or a mixture of nickel carbonate and nickel hydroxide, thereby forming a slurry after carbonation including the precipitate and a solution after carbonation; (2) solid-liquid separation step, separating the slurry after carbonation formed in the carbonation step into the precipitate and the solution after carbonation; and (3) neutralization step, adding a neutralizing agent into the solution after carbonation separated through the solid-liquid separation step to recover Ni contained in the solution after carbonation as a Ni-precipitate.