Abstract: The full approximation storage (FAS) multigrid algorithm is applied in conjunction with the artificial compressibility method to accelerate steady solutions of the 3D incompressible Navier Stokes equations. Neumann boundary conditions in terms of the solution correction are implemented on the coarse grid when solving the coarse grid equations. The basic scheme used is the diagonalized approximate factorization scheme, and the spatial difference for inviscid fluxes adopts both MUSCL scheme and symmetric TVD scheme respectively for comparing. The performance of the present method is studied for the entry flow through a 90° bent square duct and the flow past an inclined prolate spheroid with an axes ratio of 4:1. It is found that the proposed multigrid method can save the computing time by at least half, and that MUSCL scheme is slightly better than TVD scheme in resolving the flow structures.