A new copper(II) complex, [Cu(Bphen)(Leu)(NO3)(H2O)] (Bphen=4,7-diphenyl-1,10-phenanthroline, leu=L-leucine), has been synthesized and characterized by IR spectroscopy, CHN analysis, and single-crystal X-ray diffraction techniques. The CT-DNA binding properties of the complex have been investigated by both absorption and emission spectroscopy. The binding parameters for the fluorescence Scatchard plot were also determined. Further, the interaction of the complex with bovine serum albumin (BSA) has been investigated using absorption and emission spectroscopy. The thermodynamic parameters, free energy change (G), enthalpy change (H), and entropy change (S), were calculated by the van't Hoff equation and discussed. The distance between BSA and the complex has been obtained according to fluorescence resonance energy transfer. Conformational changes of BSA have been observed from synchronous fluorescence. Antioxidant and radical scavenging activities of the complex were determined by various in vitro assays such as 1,1-diphenyl-2-picryl-hydrazyl free radicals (DPPH), 2,2-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) radicals (ABTS(+)), and reducing ability determination by H2O2 scavenging methods.