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An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is described. The method is based on a correction scheme and implicit relaxation procedures and is applied to two‐dimensional test cases. The principal feature of the flow solver is a Godunov‐type averaging procedure based on the eigenvalues analysis of the Euler equations by means of which the inviscid fluxes are evaluated at the finite volume faces. Viscous fluxes are centrally differenced at each cell face. The performance of NSFLEX‐MG is demonstrated for a large range of Mach numbers for compressible inviscid and viscous (laminar and turbulent) flows over a RAE‐2822 airfoil and over a NACA‐0012 airfoil.