Abstract: Three dimensional turbulent flows with strong shock wave-boundary layer-seperated flow interactions are numerically simulated.Time-dependent compressible Navier-Stokes equations in conjunction with Baldwin-Lomax turbulence model are discrete with finite volume method and LUSGS time marching scheme to get the steady flowfields.Inviscid flux and viscous flux on the control volume surfaces are calculated with Van Leer flux vector splitting scheme and central difference scheme separatelly.The numerical methods are valid for 3D transonic flow through a diffuser.The computational results are in a good agreement well with the experimental data of Mach number before the shock wave,separation and reattachment positions.