When a flow over backward-facing step includes both subcritical and supercritical flow, the wave jump or the submerged jet occurs in that flow field. This paper presents the 2-dimensional numerical simulations of such complex flow over backward-facing Step. The numerical model is based on MacCormack scheme, and FAVOR method is introduced to the basic equations. The velocities, water depth, and the non-static pressure are computed. The numerical results are in good agreement with the experimental ones for the wave jump, submerged jet, and the shift process of each flow.