Development of nanomaterials with multiple enzymatic activities via a facile approach receives growing interests in recent years. Although peptide self-assembling provides an effective approach for the construction of biomimetic materials in recent years, fabrication of artificial enzymes from self-assembling peptides with multiple catalytic activities for anticancer therapy is still a challenge. Here, we report a simple method to prepare nanocatalysts with multienzyme-like activities from self-assembling peptides containing ATCUN copper-binding motifs. With the aid of the coordination interactions between the ATCUN motif and Cu(II) ions, these peptides could perform supramolecular self-assembly to form nanomaterials with biomimetic peroxidase, ascorbate oxidase and glutathione peroxidase activities. Moreover, these trienzyme-like effects can elevate oxidative stress levels and suppress the antioxidative capability of cancer cells, which synergistically induce the apoptosis of cancer cells. Because of the high biocompatibility, catalytic activities and drug encapsulation properties, this self-assembled peptide provides a biomimetic platform for the development of new nanocatalytic medicines for multimodal synergistic cancer therapies.