In this paper, a new approach is proposed to analyse the stability of high-order staggered-grid finite difference schemes for the three-dimensional (3D) poroelastic wave propagation. The standard staggered-grid schemes with different order accuracy in space are constructed based on the first-order hyperbolic velocity-stress system of the governing equations (i.e., Biot's equations). The new analysis method is based on von Neumann analysis. The obtained 3D stability is an explicit restriction for time step, which only depends on the coefficients of the difference operators and the material parameters of poroelastic media and so it can be computed easily. Moreover, the analysis has good generality and can be applied directly to the staggered-grid schemes for 3D elastic wave. Numerical computations with the perfectly matched layer in split formation are implemented to illustrate the effectiveness of the schemes for 3D poroelastic wave propagation. The method in this paper can be expected to analyse the stability for other staggered-grid schemes.