This paper primarily investigates the relationship between the wake vortices and vortex-induced vibrations in hydrofoil structures, as well as explores effective methods to suppress structural vibrations in hydrofoils using a piezoelectric control system. By combining CFD simulations with PIV experiments, the study compared the vortex characteristics at the trailing edge of hydrofoils with different geometries. Furthermore, by integrating the results from the water tank experiments, the research revealed the sensitivity of vortex-induced resonance to the regularity and periodicity of the von Kármán vortex street. Subsequently, the FxLMS algorithm was fine-tuned based on a phenomenological model of vortex-induced resonance. Active control experiments on vortex-induced vibrations of the hydrofoil were conducted using a piezoelectric control system built on this algorithm, achieving a maximum vibration reduction rate of 56%. Finally, the instability and limitations of the control effectiveness were analyzed, and future research directions were proposed to improve control strategies and the system's temporal responsiveness.