We report a detailed first-principles calculation to investigate the structures, elastic constants, and phase transition of Ti. The axial ratios of both a-Ti and w-Ti are nearly constant under hydrostatic compression, which confirms the latest experimental results. From the high pressure elastic constants, we find that the a-Ti is unstable when the applied pressures are larger than 24.2 GPa, but the w-Ti is mechanically stable at all range of calculated pressure. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening around point of w-Ti. When the pressure is raised to 35.9 GPa, the frequencies around the point along-M-K and -A in transverse acoustical branches become imaginary, indicating a structural instability. Within quasiharmonic approximation, we obtained the full phase diagram and accurate thermal equations of state of Ti. The phase transition w-Ti→a-Ti→b-Ti at zero pressure occurs at 146K and 1143K, respectively. The predicted triple point is at 9.78 GPa, 931 K, which is close to the experimental data. Our thermal equations of state confirm the available experimental results and are extended to a wider pressure and temperature range.