A novel naphthalene-2,3-diamine-2-salicylaldehyde (NS) ligand and its mononuclear copper(II) complex (CuNS) have been synthesized and structurally characterized. The UV-vis absorption and emission spectra of NS showed obvious changes on addition of Cu2+ solution. The interaction of the compounds with calf thymus DNA and G-quadruplex DNA were investigated by spectroscopic methods and thermal melting assay. The nucleolytic cleavage activity of the compounds was investigated on double-stranded circular pBR322 plasmid DNA and G-quadruplex DNA by electrophoretic mobility shift assay. The results show that CuNS has a greater ability to stabilize G-quadruplex DNA over calf-thymus DNA. The cytotoxicity of the compounds toward HpeG2 cancer cells was also studied, and they showed significant potential for antineoplastic effects.