A new one-dimensional copper(II) polymer, [Cu4(dmapox)2(SCN)4(CH3OH)2]n, where dmapox is the dianion of N,N′-bis[3-(dimethylamino)propyl]oxamide, was synthesized and characterized by elemental analysis, conductivity measurement, IR, and electronic spectral studies. The crystal structure of the copper(II) complex has been determined by X-ray single-crystal diffraction. The complex crystallizes in triclinic, space group P − 1 and exhibits infinite one-dimensional copper(II) polymeric chain bridged both by bis-tridentate μ-trans-dmapox and μ-1,3-thiocyanato ligand. The environment around the copper(II) atom can be described as distorted square-pyramid. The Cu···Cu separations through the oxamidate and thiocyanato bridges are 5.246(2) Å (Cu1–Cu1i), 5.2649(14) Å (Cu2–Cu2ii), and 5.8169(15) Å (Cu1–Cu2), respectively. The interaction of the copper(II) complex with herring sperm DNA (HS-DNA) has been investigated by using absorption and emission spectral and electrochemical techniques and viscometry. The results reveal that the copper(II) complex may interact with DNA in the mode of groove binding with the intrinsic binding constant of 2.56 × 105 M−1.