Proteasome inhibitors are useful for biochemical research and clinical treatment. In our previous study, we reported that the 4N-coordinated platinum complexes with anthracenyl ring and heterocycle exhibited proteasome-inhibitory activity. In the present study, the structure–activity relationships and characterization of these complexes were determined for the elucidation of the role of aromatic ligands. Lineweaver–Burk analysis revealed that the chemical structure of heterocycles affects the binding mode of platinum complexes. Platinum complexes with anthracenyl ring and pyridine showed competitive inhibition, although platinum complexes with anthracenyl ring and phenanthroline showed non-competitive inhibition. The structure–activity relationships demonstrated that anthracenyl moiety plays a crucial role in proteasome-inhibitory activity. The platinum complexes with naphthyl or phenyl rings exhibited lower inhibitory activities than the platinum complex with anthracenyl ring. The reactivity with N-acetylcysteine varied according to the chemical structure of complexes.