This study employs an incompressible homogeneous flow framework with a transport-equation-based cavitation model and shear stress transport turbulence model to successfully reproduce the unsteady cavitating flow around a three-dimensional hydrofoil. Cavity growth, development, and break-off during the periodic shedding process are adequately reproduced and match experimental observations. The predicted shedding frequency is very close to the experimental value of 23 ms. By monitoring the motions of the seeding trackers, growth-up of attached cavity and dynamic evolution of U-type cavity are clearly displayed, which indicating the trackers could serve as an effective tool to visualize the cavitating field. Repelling Lagrangian Coherent Structure (RLCS) is so complex that abundant flow patterns are highlighted, reflecting the intricacy of cavity development. The formation of cloud cavities is clearly characterized by the Attracting Lagrangian Coherent Structure (ALCS), where bumbling wave wrapping the whole shedding cavities indicates the rotating transform of cavities and stretching of the wave eyes shows the distortion of vortices. Generation of the re-entrant jet is considered to be not only associated with the adverse pressure gradient due to the positive attack angle, but also the contribution of cloud cavitating flow, based on the observation of a buffer zone between the attached and cloud cavities.