A series of platinum(II) complexes, with N-monosubstituted 1R,2R-diaminocyclohexane bearing methoxy-substituted benzyl groups as carrier ligands, were designed and synthesized. The newly prepared compounds, with chloride anions as leaving groups, were found to be very active against the tested cancer cell lines, including a cisplatin-resistant cell line. Despite their efficacy against tumor cells, they also showed low toxicity to a human normal liver cell line. Among them, complex 1 had superior cytotoxic activity against A549, HCT-116, MCF-7, SGC7901, and SGC7901/CDDP cancer cell lines. The DNA binding assay is of further special interest, as an unusual monofunctional binding mode was found, due to the introduction of a rigid substituted aromatic ring in the 1R,2R-diaminocyclohexane framework as steric hindrance. The linkage of complex 1 with DNA was stable and insensitive to nucleophilic attack. Moreover, studies including cellular uptake, gel electrophoresis, apoptosis and cell cycle, and Western blot analysis have provided insight into the high potency of this compound.