In the current paper, large eddy simulation is utilized to study the effect of various wavy leading edges on the control of cavitation around a modified NACA634-021 hydrofoil in the case of equal lift. Four sinusoidal wavy leading edges with different geometry parameters are numerically examined, with the baseline hydrofoil as a comparison. The numerical results are compared with available experimental data and a reasonable agreement is observed. The key flow characteristics, e.g., quasi-periodic behavior of cavity, time histories of pressure fluctuations and the effect of cavitation on streamwise vortices are compared in detail. The results show that in the case of equal lift, which is achieved by adjusting the angle of attack, no significant decrease in the volume of cavity is observed for the cases of wavy leading edges. This illustrates that none of the four different types of wavy leading edges introduced in this paper can appreciably suppress the generation and development of cavitation bubbles. However, our results indicate that the pressure fluctuations can be effectively suppressed, which is primarily caused by the compartmentalization effect of the leading edge protuberances. Meanwhile, the suppression capability decreases with an increasing amplitude-to-wavelength ratio. Further analysis shows that cavitation is the main source of affecting the development of the streamwise vortices. •The cavitating hydrofoils with various wavy leading edges are studied by LES.•The cavity volume is not effectively suppressed by wavy leading edges in the case of equal lift.•The pressure fluctuations can be effectively suppressed by wavy leading edges.