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.