Abstract: Based on the MacCormack explicit difference Scheme,a multigrid scheme has been developed to solve the three dimensional Euler equations expressed by weak conservation law in cylindrical coordinate system.The distribution and interpolation formulas of corrections for the presented multigrid scheme have been derived.The present Euler solver was used to calculate the flows of two sets of transonic compressor rotor blade rows,and proven to be a valid and useful design tool.The computed results indicate that this scheme is enable to accelerate the computation convergence greatly,and the method is accurate and reliable.