The constrained interpolation profile (CIP) method, a type of method of characteristics (MOC), is a novel low-dispersive numerical scheme. In an earlier study, we applied the CIP method to quantitative analyses of sound wave propagation. However, a new grid system is important for the CIP simulation of complicated heterogeneous media or large-scale simulations of wave propagation. In this study, we examined a subgrid technique for use with acoustic wave simulation using the type-M and type-C CIP methods. The results indicate that this technique for the CIP methods has advantages of small memory requirements and faster calculation.