A two-dimensional preconditioned multigrid Navier-Stokes solver has been developed for all Mach number viscous flows. For the computation of all Mach number flows, a local preconditioning technique with a modified reference velocity was used to extend the Harten-Lax-van Leer-Einfeldt(HLLE+) scheme, which has good characteristics for compressible viscous flows. The developed methods used to compute several representative steady problems. Grid refinement and parametric studies are performed to verify the performance. The results show that the preconditioned HLLE+ scheme can be successfully applied to a wide variety of flows and that the implicit multigrid solver provides good convergence for the test problems.