Abstract: An implicit finite-difference method based on the SMAC (Simplified Marker and Cell) scheme for directly solving incompressible unsteady N-S equations is developed. The method is based on the contravariant velocities and the elliptical Poisson pressure equations in general curvilinear coordinates. Numerical results for two-dimensional unsteady separated flows through a cascade are shown. The computed results of the surface pressure coefficient are in satisfactory agreement with the experimental data. The structure of flow fields and the mechanism of unsteady flows are investigated preliminarily. The numerical results indicate that the flows are strong unsteady flows, though the inlet velocity is mean and the boundary conditions are steady. When the angle of attack is small and the Reynolds number is high, periodic fluctuating flow similar to the Kármán vortex street is formed at the trailing edge.