In this paper, the cavitating flow over a flexible NACA66 hydrofoil is studied numerically by a modified fluid-structure interaction strategy with particular emphasis on understanding the flow-induced vibration and the cavitating vortical flow structures. The modified coupling approaches include (1) the hydrodynamic solution obtained by the large eddy simulation (LES) together with a homogenous cavitation model, (2) the structural deformation solved with a cantilever beam equation, (3) fluid-structural interpolation and volume mesh motion based on the radial basis functions and greedy algorithm. For the flexible hydrofoil, the dominant flow-induced vibration frequency is twice of the cavity shedding frequency. The cavity shedding frequency is same for the rigid and flexible hydrofoils, demonstrating that the structure vibration is not large enough to affect the cavitation evolution. The predicted cavitating behaviors are strongly three-dimensional, that is, the cavity is (a) of a triangular shape near the hydrofoil tip, (b) of a rectangular shape near the hydrofoil root, and (c) with a strong unsteadiness in the middle of the span, including the attached cavity growth, oscillation and shrinkage, break-off and collapse downstream. The unsteady hydroelastic response would strongly affect the cavitation shedding process with small-scale fragments at the cavity rear part. Furthermore, three vortex identification methods (i.e., the vorticity, the Q- criteria and the omega method) are adopted to investigate the cavitating vortex structures around the flexible hydrofoil. It is indicated that the cavity variation trend is consistent with the vortex evolution. The vortex structures are distributed near the foil trailing edge and in the cavitation region, especially at the cavity-liquid interface. With the transporting downstream the shedding cavities, the vortices gradually increase in the wake flows.