A multistep characteristic-based operator-splitting finite element method is proposed to determine the effects of adding a splitter plate at the back of a cylinder on the characteristics of a flow past a circular cylinder. In each time step, the N-S equations are split into diffusive and convective parts. For the convective part, temporal discretization is performed by the characteristic Galerkin method with a multistep technique. Results of the present model are in good agreement with previously published data. Thus, the present model is competitive in solving incompressible viscous flows in terms of accuracy and efficiency. Furthermore, the flow past a circular cylinder with a splitter plate was simulated by the present model. The flow fields and pressure on the cylinder surface with and without a splitter plate were compared. Findings indicated that the plate can suppress vortex shedding, increase the pressure on the leeward of the cylinder, and reduce the pressure difference between the upper and lower surfaces.