Abstract: A novel finite element method, which is projection/Characteristic-based operator-splitting finite element method, is proposed for the prediction of unsteady incompressible N-S equations. In each time step, the equations are split into the diffusive part, the convective part and the pressure correction part. The temporal discretization of the convective part is performed by an exact characteristic-Galerkin method. The convective part is solved explicitly and a multistep technique is introduced to enlarge the calculation precision. The plane Poisseuille flow, the driven square flow and the flow over a circular cylinder are conducted to validate the model. It is show that the numerical results are close to reference results. In particularly, for the driven square flow at Re=10000, the flow becomes periodical in time and small vortex structure can be simulated.