To develop high-performance medical alloy coatings that can reduce the risk of postoperative infection, TiZrNbCux refractory medium-entropy alloy (RMEA) coatings are designed and prepared on the Ti6Al4V alloy. The effects of varying Cu additions on the microstructure, micro/nano-hardness, elastic modulus, wear resistance, corrosion resistance, and antibacterial properties are investigated. The microstructure reveals that the RMEA coatings comprise body-centered-cubic dendrites and an Mo2Si-type interdendritic (Ti, Zr)2Cu phase. Also, the contents and dimensions of (Ti, Zr)2Cu gradually increase with the increasing Cu contents. The increased amounts of Cu atoms are beneficial for the improvement of hardness and elastic modulus, but contribute little to wear resistance. Meanwhile, the electrochemical polarization curve reflects that Cu-containing RMEA coatings show superior corrosion resistance. The antibacterial test on the Cu0.1 RMEA coating demonstrates a 99.95% antibacterial rate against S. aureus after coculturing for 18 h, indicating its novel antibacterial property. Thus, TiZrNbCux RMEA coatings present huge potential in medical applications for implants.