The local structure of the perovskite KNbO3 at 77 K and 300 K under high pressure, up to 15.8 GPa, h~s been investigated using the X-ray absorption fine structure (XAFS) technique. We found that local distortions exist throughout the measured range which are peaked off-center at the rhombohedral symmetry sites with a width narrower than the separation between the rhombohedral and orthorhombic sites. On the other hand, diffraction indicates an orthorhombic average structure at 300K, and optical measurements suggest a transition to a cubic phase at high pressures. To explain the difference between pressure-induced changes in KNb03 structure as measured by XAFS and optical techniques, a pressure-dependent hopping rate in the framework of the eight-site model is proposed.