A novel numerical method solves the VIScous Vorticity Equation (VISVE) in 3D in order to model the Leading Edge Vortex (LEV) of propellers is proposed and implemented in this dissertation. The spatial concentration of the vorticity is exploited in the method, which is designed to be spatially compact and numerically efficient, in the meantime, capable of modeling complicated vorticity/solid boundary interaction in 2D and 3D. The numerical model can work as a viscous correction on top of the traditional Boundary Element Method (BEM) results. The proposed method is first applied in the case of a 2D hydrofoil at high angle of attack. The results are correlated with those from Navier-Stokes (N-S) simulation. The method is then used to model the LEV and tip vortex of a 3D swept wing. The results of the 3D simulation show great similarity to those from N-S. In the end, the method is applied in the case of propellers at low advance ratios. All the essential flow characteristics (LEV and tip vortex) are predicted. The objective of this dissertation is not developing a mathematically equivalent numerical method to the full-blown Reynolds-Averaged Navier-Stokes (RANS) solver, but inventing an accurate and computationally efficient tool to model the effects of the LEV on the propeller performance for engineering's purpose. / text