Monolayer WS2, MoS2 and ZrS2 with excellent mechanical properties were coated on the copper surface to improve the anti-wear ability. Their nano-tribological models sliding with copper under the same condition were developed by molecular dynamics (MD) simulation to deeply reveal the anti-wear mechanisms. Firstly, the mechanical response of the copper substrate with different coatings in the tip indentation process was investigated. Importantly, the friction reduction mechanism of the WS2, MoS2 and ZrS2 was revealed by extracting and analyzing the friction coefficient, the interfacial van der Waals (vdW) force, the interface temperature, the energy of system and the friction morphology during the friction process from the nanoscale. Von Mises stress distributions on the copper substrate at different stages were also investigated to virtually observe the change of atoms. The simulated results indicated that copper layer coated by WS2 had the best anti-wear effect among the three materials because of its excellent ability to reduce the interaction between C atoms and Cu atoms.