First-principles density-functional method is used to study the recently high-pressure synthesized compound PtC. It is confirmed by our calculations that the platinum carbide has a zinc-blende ground-state phase at zero pressure and the rock-salt structure is a high-pressure phase. The theoretical transition pressure from zinc-blende to rock-salt is determined to be 52GPa. Furthermore, our calculation shows the possibility that the experimentally synthesized PtC by Ono et al. under high pressure condition might undergo a transition from rock-salt structure to zinc-blende after the pressure quench to ambient condition. PACS number(s): 62.50. +p, 71.20. Ps, 81.05. Zx