Five innovative ternary copper (II) complexes [Cu (OH‐PIP)(Phe)Cl](1), [Cu (OH‐PIP)(Gly)(H2O)]NO3·2H2O (2), [Cu (OH‐PIP)(Ala)(Cl)]·H2O (3), [Cu (OH‐PIP)(Met)]PF6·2H2O (4), and [Cu (OH‐PIP)(Gln)(H2O)]Cl·3H2O (5) have been synthesized and characterized by infrared spectroscopy, elemental analysis, and single crystal X‐ray diffraction analysis. X‐ray crystallography showed that all Cu atoms were five‐coordinated in a square‐pyramidal configuration. They are screened for in vitro cytotoxicity against a panel of human cancer cell lines CAL‐51, MDA‐MB‐231, HeLa, MCF‐7, SGC‐7901, A549, K562, and SMMC‐7721. The most promising results were achieved for complexes 1 to 5, with the IC50 values in the range of 0.082μM to 0.69μM (against CAL‐51 cell lines). The anticancer activities against CAL‐51, MDA‐MB‐231, and MCF‐7 were higher than that of Carboplatin. The mechanism studies showed that complexes 1 to 5 could inhibit proteasome activity, induce apoptosis, and inhibit cell proliferation, indicating their great potential as proteasome inhibitors for triple‐negative breast cancer therapy.