Motivated by the experimental huge enhancement of the superconducting transition temperature T c in FeSe superconductor under high pressure, we perform first-principles calculations of the evolutions of structural, electronic, and lattice dynamical properties of FeSe at varying hydrostatic pressures up to 8 GPa. The pressure response is anisotropic with a larger compressibility along c-axis. At ambient pressure, Fermi surface nesting between hole and electron pockets induces spin density wave (SDW) order at the vector (π , π , 0) with a collinear antiferromagnetic structure. With the increase of pressure, the Fermi surface nesting is reduced, and therefore the SDW is suppressed, which could not enhance superconductivity based on the spin-fluctuation scenario. For the phonon dispersion, the bands have blue-shift except for the modes around 100 cm −1 , indicating hardening of the vibration modes in a wide frequency range. Furthermore, the electron-phonon coupling constant and the corresponding T c by McMillan equation are calculated. However, there is no obvious enhancement of T c under pressure, which further rules out the conventional phonon-mediated superconductivity of FeSe. Maybe the local magnetic moment plays an important role for the superconductivity and enhancement of T c under pressure.