Molecular dynamics simulation is used to study the thermal stability of cubic platinum nanoparticle. The simulated results show that the cubic nanoparticle first transforms into the truncated cube enclosed by {111} and {100} facets, and then transforms to the spherical one. Finally, it melts into liquid state. The critical temperature of shape transformation is about 1250 K according to the calculation of statistical radius. Cubic and spherical nanoparticles have the same melting point in spite of their different shapes.