This paper aims at developing an incompressible N-S equation solver for two -dimensional compressor cascade flows with massive separation for engineering applications. A staggered grid system different from that of SIMPLE method is proposed to make discretization and implementation of boundary conditions very simple and to reduce the computational efforts needed for a two- or three-dimensional problem nearly to the efforts for one-dimensional one. To ensure the numerical stability of convection-diffusion equations

a so-called upwind factor method is devised

which is robust and accurate. To deal with the determination of the pressure field an algebraic pressure correction expression is derived to simplify the numerical scheme further.To verify the scheme four different compressor cascades are taken as examples for numerical experiments. The incident angle varies from -13 to +11. The numericalresults of the deviation angle and separation point are compared with the corresponding physical experimental data in good agreements.