The star formation rate in the Milky Way has remained at about 1 solar mass per year for about 8 billion years, and this mechanism has not been clarified. Recently, it is considered that star formation is maintained by the gas circulation between the galactic disk and the galactic halo. The detailed theoretical calculations of the gas transport mechanism from the galactic plane to the halo were performed by Shimoda and Inutsuka (2022). However, the quantitative study of the gas “fallback” mechanism remains to be done. Smoothed Particle Hydrodynamics (SPH) is supposed to be a useful method for describing this phenomenon. This method has the advantage of describing high-density regions with high accuracy. In other words, it has the disadvantage of low accuracy in low-density regions. When we use SPH particles of equal mass to describe two phases with very different densities, for example, Cold Neutral Medium (CNM) and Warm Neutral Medium (WNM), simultaneously, there is a large difference between the resolution of the CNM and that of the WNM. Thus, the interaction between them cannot be accurately described. This is a problem in accurately describing the interaction and transformation between them. On the other hand, the formulation for the case of non-equal mass SPH particles has not been well examined. In this study, we develop a volume-based SPH as a new SPH method for non-equal mass particles. In this poster, we introduce the concept of the volume-based SPH and derive the time evolution equation for particles. The capability of the method is demonstrated by many test calculations.