The application of Large Eddy Simulation (LES) in a curvilinear coordinate system to the flow around a square cylinder is presented. In order to obtain sufficient resolution near the side of the cylinder, we use an O-type grid. Even with a curvilinear coordinate system, it is difficult to avoid the numerical oscillation arising in high-Reynolds-number flows past a bluff body, without using an extremely fine grid used. An upwind scheme has the effect of removing the numerical oscillations, but, it is accompanied by numerical dissipation that is a kind of an additional sub-grid scale effect. Firstly, we investigate the effect of numerical dissipation on the computational results in a case where turbulent dissipation is removed in order to clarify the differences between the effect of numerical dissipation. Next, the applicability and the limitations of the present method, which combine the dynamic SGS model with acceptable numerical dissipation, are discussed.