Large eddy simulations of tip vortex cavitation (TVC) around an elliptical hydrofoil is performed to study its scale effect. A satisfying agreement is obtained between the numerical and experimental data. It indicates that the scale effect of TVC is remarkable. With the increase of scale ratio or incoming velocity, the intensity of TVC significantly increases. Based on our results, two mechanisms for the scale effect of TVC are proposed, i.e., the roll-up of boundary layer and the interaction between tip vortex (TV), secondary vortex and trailing vortex. As incoming velocity increases, the fusion of TV and secondary vortex enhances and the boundary layer thickness decreases, which lead to larger circulation and smaller vortex core radius, tending to intensify TV. As scale ratio increases, the fusion of TV and secondary vortex enhances and the boundary layer thickness increases slightly, which lead to much higher circulation and slight increase of vortex core radius, promoting the occurrence of TVC in general. In addition, with equal cavitation number and Reynolds number, TVC in the large scale is stronger than that in the small scale, indicating that it seems not so reasonable to equate the velocity-induced scale effect with the scale-ratio-induced one.