The ReO3-type structure NbO2F, niobium dioxyfluoride, has been studied at high pressures using diamond anvil cells and synchrotron X-ray radiation. High-pressure powder diffraction measurements have been performed up to 40.1 GPa. A phase transition from the cubic (Pm3m) ambient pressure structure to a rhombohedral (R3c) structure at 0.47 GPa has been observed. Rietveld refinements at 1.38, 1.96, 3.20, 6.23, 9.00 and 10.5 GPa showed that the transition involves an a-a-a- tilting of the cation-anion coordination octahedra and a change of the anion-anion arrangement to approach hexagonal close packing. Compression and distortion of the Nb(O/F)6 octahedra is also revealed by the Rietveld refinements. At 17-18 GPa, the diffraction pattern disappears and the structure becomes X-ray amorphous.