This paper concerns a parallel computation method for advection-diffusion equations using a distributed memory system. The governing equations discretized with a finite difference method are solved with a domain decomposition method which has overlap grid points. The advection terms are discretized with a. QSI scheme and upwind difference methods to compare their accuracy and efficiency. The computational time and speedup are modeled with the numbers of the grid points, Nc and Nm, which are used in the computations and message passing respectively, in addition to the processor number p. As a result of the parallel computations, it has been shown that the proposed model reasonably represents the characteristics of the speedup and that the parallel computation is particularly advantageous in the QSI scheme in terms of the speedup and numerical accuracy.