In this paper, based on the boundary approximation approach for parallelization of the compact difference schemes, a novel strategy for the sub-domain boundary approximation schemes is proposed to maintain consistent accuracy and dispersion with the compact scheme in the interior points. In this strategy, not only the order of accuracy of the sub-domain boundary scheme is the same as the interior scheme, but the coefficient of the first truncation error term is also equal to that of the internal scheme. Furthermore, to realize the consistent dispersion performance for a class of high order upwind compact schemes, which usually include two expressions, we modify the opposite expression to be the sub-domain boundary scheme. As an example of application, the present strategy is applied to a fourth-order upwind compact scheme, and its accuracy is verified by a numerical test. The resolution and efficiency of the newly proposed parallel method are examined by four numerical examples, including propagation of a wave-packet, convection of isentropic vortex, Rayleigh–Taylor instability problems, and propagation of Gauss pulse. The results obtained demonstrate that the present strategy for compact difference schemes has the feasibility to solve the flow problems with high accuracy, resolution and efficiency in parallel computation.