Abstract: An implicit Navier-Stokes solver is presented for numerical simulation of three-dimensional steady compressible turbulent flow in a transonic compressor stage.The LU-SGS(Low-Upper Symmetric-Gauss-Seidel)implicit time-marching scheme developed by Jameson and Yoon is used to improve the computational efficiency.In order to obtain distinct shock system and valid boundary layer characteristics,one kind of high resolution schemes,the third order accurate NND (Non-oscillatory,Non-free-parameter,Dissipative)scheme is incorporated in this solver.The governing equations,the numerical scheme,the grid system and the boundary treatment method are considered in this paper.The Baldwin-Lomax Algebra model is utilized to compute the turbulent viscosity.The viscous flow in a single stage transonic compressor is calculated by this solver.The calculation was performed by coupling the rotor and stator flow fields at each time step through an overlapped grid.The computed results were compared with experiment data.