Abstract: The laminar N S equations have been solved for a supersonic flow with a transverse sonic jet.The numerical algorithm used here is a second order windward TVD scheme.The conditions of supersonic main stream are: Ma ∞=2 5,T ∞ =130K, Re ∞=5×10 5.In sonic jet, T j=243(T j/T ∞=1 87),P j/P ∞ =43 0.The grid nodes are 121×95 with compressed in both a transverse direction near the wall and a straemwise direction near the injector.The detail waves and vortex structures are obtained,the flow field pictures and pressure distribution along plate are compared with experiments in a good agreement.The calculation also demonstrates that the TVD scheme not only has high capability of shock capturing,but also can be applied to efficient simulation of the complex vortex structure.