Ten 4′- (R-phenyl) -2,2′: 6′, 2′ – terpyridine ligands (R = hydrogen (L1), hydroxyl (L2), methoxyl (L3), methylsulfonyl (L4), methyl (L5), phenyl (L6), fluoro (L7), chloro (L8), bromo (L9), and iodo (L10)) were synthesized. The reaction of these ligands with copper(II) nitrate led to complexes 1–10. The characterization of 1–10 was carried out by means of mass spectrometry, elemental analysis, infrared spectroscopy and X-ray single crystal diffraction. Four cell lines including esophageal cancer cell line (Eca-109), human liver cancer cell line (Bel-7402), human breast cancer cell line (SIHa) and human normal liver cell line (HL-7702) were selected to carry out antiproliferation and cytotoxicity experiments in vitro. The results showed that the complexes have strong inhibitory ability on the growth of tumor cells. In order to study the anticancer mechanism of the complexes, the binding mode and binding ability of the complexes with DNA were further determined and discussed with UV–Vis spectroscopy and circular dichroism. The effects of the lowest binding energy and hydrogen bond on the binding were studied using molecular docking calculation.