In this paper, we have examined the thermal stability of Pt-Au core-shell nanoparticle by using molecular dynamics simulations with embedded-atom potential. The results show that the melting point of Pt-Au core-shell nanoparticle is significantly higher than that of pure Au one but lower than that of Pt one. By the analyses of Lindemann index, it is discovered that the melting first occurs in Au shell, then spreads into interior, finally the overall melting of Pt core appears. The temperature range of melting is much broader for Pt-Au core-shell nanoparticle than for Au and Pt nanoparticles. Moreover, Pt-Au core-shell nanoparticle exhibits a distinct two-stage melting during continuous heating, and the structure of solid (core)-liquid (shell) coexistence has been observed between two meltings.