A numerical approach based on a finite element method has been developed to simulate the two-dimensional blade-vortex interaction in viscous flows. In the scheme, the incompressible Navier-Stokes equations in the vorticity-stream form are used. When the passing vortex is approaching the airfoil from upstream, two different models for the vortex are used. Firstly, the vortex is modeled as an ivicsid vortex convecting at the speed of the local fluid, and the total flow is the superposition of the vortex-induced flow and the viscous flow. Secondly, when the vortex is close to the airfoil, it is distributed in a weighted manner at the nodes of the element where it is located, and then the total flow is governed by the Navier-Stokes equations. Some numerical results are presented, and the potential of the present work is discussed.