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.