Abstract: Regarding a viscous shock wave in a high pressure metal as a strong discontinuity, Miller G H, et al pointed out that a little perturbation shock was unstable under little Reynolds number or large viscosity, and material viscosity was a destabilized factor. Aimed at the conclusion by Miller G H, et al, the linear stability theory was adopted to discuss the stability of normal shock waves in a viscous metal. Regarding a viscous normal shock wave in a high-pressure metal as a continuous profile, this paper points out that any little perturbation shock is stable under any Reynolds number, and material viscosity is a stabilized factor. The error by Miller G H, et al was demonstrated that the boundary conditions from inviscid solutions could lead to the increase of a little perturbation shock. An experimental boundary condition was given to guarantee the stability of a viscous normal shock wave. So a viscous normal shock wave can be regarded as a strong discontinuity, and its stability can be guaranteed.