Spherical-shape melanin nanoparticles with good water-dispersibility were successfully synthesized by a simple oxidation polymerization of 3,4-dihydroxy-phenylalanin (DOPA) with $KMnO_4$. Similar features to those known from natural and synthetic melanin polymers were observed from prepared melanin nanoparticles by FT-IR, UV-Vis., and ESR spectroscopic methods. Their binding ability with several heavy metal ions from aqueous solution was quantitatively investigated, and the maximum binding capacities with melanin nanoparticles to lead, copper, and cadmium ions were obtained as 2.45, 2.17 and 1.88 mmol/g, respectively, which are much larger values than those reported from natural and synthetic melanin polymers. The large binding capacity and fast binding rate of melanin nanoparticles to metal ions can make them an excellent candidate for the remediation of contaminated water.