A selected chemical library of six platinum(II) complexes having 1,2-bis(aminomethyl)carbobicyclic ligands were synthesized after a rational design in order to evaluate their antiproliferative activity and the structure-activity relationships. The cytotoxicity studies were performed using cancer cell lines sensitive (A2780) and resistant (A2780R) to cisplatin. Excellent cytotoxicity was observed for most of complexes, which presented better resistance factors than cisplatin against the A2780R cell line. The interaction of these complexes with DNA, as the target biomolecule, was evaluated by several methods: DNA-platinum binding kinetics, changes in the DNA melting temperature, evaluation of the unwinding angle of supercoiled DNA, evaluation of the interstrand cross-links, and replication mapping. The kinetics of the interaction with glutathione was also investigated to better understand the resistant factors observed for the new complexes.