Recently Wu Z N and Zou H proposed an overlapping grid method.The suitability of applying the method to parallel computation of steady and unsteady compressible inviscid flows with three-point block-tridiagonal implicit schemes was addressed in the paper [1],and an easily usable interface treatment was constructed and analyzed for both steady and unsteady problems.This method is here applied to the computation of N-S equations.In both steady and unsteady cases a good absolute parallel efficiency has been still demonstrated for bidimensional subsonic and transonic flow computations.