In this paper, we investigate the numerical stability for solving the three dimensional (3D) poroelastic wave equations with the high-order staggered-grid method. First by introducing some proper difference operators, we construct the arbitrary high-order staggered-grid schemes for 3D poroelastic wave equations with spatially varying media parameters. Then the stability condition of the schemes is derived firstly. The result is an explicit restriction of time step, which only depends on the difference coefficients and the spatially varying media parameters. The condition is sufficient and can be computed prior to numerical computations, which is very helpful for us to find suitable time step and spatial grid size in numerical computations efficiently. For numerical computations, absorbing boundary conditions with perfectly matched layer (PML) based on real prolongation variables are derived. Numerical computations of 3D poroelastic wave propagation with PML are completed. The results show the effectiveness of our developed method.