The local structure and the electronic properties of FeSe under hydrostatic pressure were studied by means of dispersive x-ray absorption measurements at the Fe K-edge. The pressure dependence of the x-ray absorption near edge structure features seems to follow the behavior of the superconducting transition temperature Tc. The local structure, that has an important impact on the superconducting properties, appears to fall into two regimes: the pressure dependence of the Fe-Fe bond distance shows a clear change in the compressibility at p ∼ 5 GPa; in contrast, the Fe-Se bond distance decreases continuously with increasing pressure with a lower compressibility than the Fe-Fe bond. The results suggest that the pressure dependent changes in Tc of FeSe are closely related to the changes in local structure.