Abstract: A time-marching finite difference method is presented for the numerical simulation of the three dimensional unsteady viscous flow by rotor-stator interaction in an axial transonic stage.A high-resolution scheme is adopted to capture flow shocks.The flow information of rotor and stator is exchanged by using the system of overlaid grids.In order to reduce CPU time,an implicit LU-SGS method is applied to obtain rapidly a steady state solution,from which an unsteady flow computaion can be started.A numerical example for a transonic compressor stage has been carried out.The results show a good prediction of the unsteady effects caused by rotor-stator interaction.