The constrained interpolation profile (CIP) method is a novel low-dispersive numerical scheme. It is a kind of method of characteristics (MOC). In our past study, we applied the CIP method to numerical analyses of sound wave propagation. For simulations of complicated heterogeneous media or large-scale simulations of wave propagation, a new grid system is indispensable. In this study, we examined a sub-grid technique for the CIP acoustic wave simulation. It is clarified that this technique has the advantages of its small memory requirements and less calculation time.