Abstract: In the present paper, the tip-leakage vortex (TLV) cavitation around a NACA0009 hydrofoil is numerically investigated with large eddy simulation method combined with a new Euler-Lagrangian cavitation model, which takes into account the effect of nuclei on tip-leakage cavitating flow. A satisfying agreement between the numerical and experimental results is obtained. Based on the numerical data, the evolution behavior of TLV cavitation with different gap sizes and its influence on the strength and radius of TLV, the nuclei distribution in the vortex core and the distribution of tangential velocity are discussed in detail. The results show that once cavitation occurs, the intensity of TLV is mainly affected by the evolution behavior of the sheet cavitation, while the tip-leakage cavitating flow has little effect on the strength of TLV. In addition, the results suggest that a smaller gap size will result in a more unstable sheet cavity, and the strength of TLV in turn presents corresponding quasi-periodic fluctuation as influenced by the evolution of the sheet cavitation. As the tip clearance progressively increases, the strength of the sheet cavitation gradually decreases with the reduction of instability, and the intensity of TLV gradually returns to the level without cavitation, together with its fluctuation level. Cavitation has a more significant influence on the nuclei distribution in the vortex core, and its degree of influence depends on the spatial stability of TLV and the intensity of TLV cavitation after the occurrence of cavitation. Moreover, the numerical results obtained by our simulations also indicate that cavitation has a significant influence on the radius of TLV. After cavitation occurs, the radius of TLV increases to a certain extent, and a ``rigid body rotation'' tangential velocity distribution is formed on the periphery of cavitation region, which is mainly caused by the expansion process induced by cavitation growth and the viscous effect of flow.