Abstract: The internal 3-D viscous flow fields of the transonic axial-flow compressors were numerically analyzed using a time-marching finite difference method.This calculation method was developed by the LU-SGS(lower-upper symmetric Gauss-Seidel) implicit scheme and NND(non-oscillatory,containing no free parameters and dissipative) scheme with Steger-Warming flux vectors splitting technique,and the centered difference scheme was used for the viscous portion.The mixing plane model was employed to simulate the internal 3-D viscous flow fields of multistage axial-flow compressors,so the overall performance for NASA rotor 37,NASA rotor 67 and one stage compressor was obtained and the internal flow fluids were analyzed in detail.As compared with experimental data,the good agreements are found,indicating the model and method are feasible and reliable.