We calculated the phase transition, elastic constants, full phonon dispersion curves, and thermal properties of molybdenum (Mo) for a wide range of pressures using density functional theory. Mo is stable in the bodycentered-cubic (bcc) structure up to 703 (19 GPa and then transforms to the face-centered close-packed (fcc) structure at zero temperature. Under high temperature and pressure, the fcc phase of Mo is more stable than the bcc phase. The calculated phonon dispersion curves accord excellently with experiments. Under pressure, we captured a large softening along H-P in the TA branches. When the volume is compressed to 7.69 A3, the frequencies along H-P in the TA branches soften to imaginary frequencies, indicating a structural instability. When the pressure increases, the phonon calculations on the fcc Mo predict the stability by promoting the frequencies along Γ to X and Γ to L symmetry lines from imaginary to real. The thermal equation of state was also investigated. From the thermal expansion coefficient and the heat capacity, we found that the quasiharmonic approximation was valid only up to about melting point at zero pressure. However, under pressure, the validity can be extended to a much higher temperature.