Incompressible viscous flows around a circular cylinder placed at various heights above a moving plate have been investigated numerically using finite difference method for the high Reynolds number (Re=5×104). A Navier-Stokes equation solver employing an overset grid system was applied to treat the complex geometry. The calculated results of lift coefficients and the Strouhal number were compared with experimental ones. It is found that the calculated results are in a good agreement with the experimental ones. Furthermore the structure of the wake behind the cylinder is made clear with the flow patterns and the pressure distributions. These results also show that due to the effects of the plate the regular vortex shedding is suppressed for all gaps less than about 0.3 times of the cylinder diameter.