According to the characteristics of compressible flows with wall boundary conditions, a simplified iterative-implicit timeadvancement scheme combined with high order compact difference schemes based on a non-uniform grid system is proposed to solve compressible Navier-Stokes equations, An iteration convergence criterion is given. The computational efficiency is greatly improved. The new scheme is applied to simulate two-dimensional compressible flat-plat laminar boundary layer flows and two-dimensional compressible channel flows.