Isothermal-isobaric ensemble Monte Carlo simulation of adamantane has been carried out with a variable shape simulation cell. The low-temperature crystalline phase and the room-temperature plastic crystalline phases have been studied employing the modified Williams potential. We show that at room temperature, the plastic crystalline phase transforms to the crystalline phase on increase in pressure. Further, we show that this is the same phase as the low-temperature ordered tetragonal phase of adamantane. The high-pressure ordered phase appears to be characterized by a slightly larger shift of the first peak toward a lower value of r in C-C, C-H, and H-H radial distribution functions as compared to the low-temperature tetragonal phase. The coexistence curve between the crystalline and plastic crystalline phase has been obtained approximately up to a pressure of 4 GPa.