The construction of supramolecular networks with novel crosslinks is of great significance in expanding their chemical structures and exploring their advanced functions. Herein, we prepare a type of [2]catenane-cored supramolecular networks based on the crosslinking of polyethylene glycol (PEG) using a heterometallic [2]catenane unit. By adjusting the molecular weight of PEG, the solubility of the networks can be tuned and gels are formed using low molecular weight PEG. The introduction of heterometallic [2]catenane offers the networks good antibacterial properties owing to the synergistic antimicrobial activity of Pt(II) and Cu(I) ions in the [2]catenane. This study provides a simple and efficient strategy for constructing supramolecular networks with topological crosslinks as antibacterial materials, which will promote the structural design and biological applications of supramolecular networks.