In the case of medical implants, foreign materials are preferential sites for bacterial adhesion and microbial contamination, which can lead to the development of prosthetic infections. Commercially biomedical TiNi shape memory alloys are the most commonly used materials for permanent implants in contact with bone and dental, and the prevention of infections of TiNi biomedical shape memory alloys in clinical cases is therefore a crucial challenge for orthopaedic and dental surgeons. In the present study, copper has been chosen as the alloying element for design and development novel ternary biomedical Ti‒Ni‒Cu shape memory alloys with antibacterial properties. The effects of copper alloying element on the microstructure, mechanical properties, corrosion behaviors, cytocompatibility and antibacterial properties of biomedical Ti‒Ni‒Cu shape memory alloys have been systematically investigated. The results demonstrated that Ti‒Ni‒Cu alloys have good mechanical properties, and remain the excellent shape memory effects after adding copper alloying element. The corrosion behaviors of Ti‒Ni‒Cu alloys are better than the commercial biomedical Ti‒50.8Ni alloys. The Ti‒Ni‒Cu alloys exhibit excellent antibacterial properties while maintaining the good cytocompatibility, which would further guarantee the potential application of Ti‒Ni‒Cu alloys as future biomedical implants and devices without inducing bacterial infections.