Energy-dispersive X-ray absorption spectroscopy at the Mo K-edge was used to study pressure-induced (up to 36 GPa) changes in the local atomic structure of 2D layered oxide α-MoO3. A linear combination analysis based on the low and high-pressure X-ray absorption near edge structure (XANES) spectra shows clear evidence of two high-pressure phases, existing at 18-25 GPa and above 32 GPa. The first transition is due to gradual decrease of the interlayer gap, whereas the second one - to its collapse and oxide structure reconstruction. The local atomic structure around molybdenum atoms at 0.2, 18.5 and 35.6 GPa was determined from the extended X-ray absorption fine structure (EXAFS) using reverse Monte Carlo calculations.