An implicit LES code utilizing the Weighted Compact Nonlinear Scheme is developed for 3D compressible Navier-Stokes equations written on generalized curvilinear coordinate system. A supersonic flowfield over a backward-facing step in three-dimensional space is then solved by the developed implicit LES code. It is shown that characteristic features of the flowfield pertinent to a supersonic flow over a backward-facing step are well captured in the computed results. Number of longitudinal vortices appears in the boundary layer region suggesting that the flowfield behind the step becomes turbulent. A fair agreement is shown for the computed pressure profile behind the step with that of the experimental data. However, comparison with the experimental data reveals that the pressure value in recirculation region becomes slightly higher and the onset of the pressure rise is slightly shifted downstream side.