Incompressible fluid analysis using the ISPH or MPS methods requires the solution of the pressure Poisson equation, and the solution of this equation takes up most of the overall computation time. In addition, the iteration number for solving pressure Poisson equations may increase as the scale of simulation model increase. This is a common problem not only in particle methods but also in implicit solver type calculation models, but it is known that in difference methods, FEM, etc., good quality preconditioning such as multigrid preconditioning can greatly improve the convergence of iterative solution methods. There are two types of multigrid preconditioners, algebraic multigridand geometric multigrid method, but there are few examples of their application in particle methods. 　In this study, we attempted to develop a framework for a geometric multigrid preconditioner for solving the pressure Poisson equation in the ISPH. First, we focused on the geometric multigrid preconditioner using background cells [3], which is used for adjacent particle search, implemented it on a multi-GPU environment. Through a simple dam-break problem, we compared the computation time between the Conjugate gradient (CG) solver with traditional preconditioner and the CG solver with geometric multigrid preconditioner and confirmed that the backgroud cell-based geometric multigrid preconditioner is effective for the ISPH method.