  We theoretically propose a second-order topological magnon insulator by
stacking the van der Waals honeycomb ferromagnets with antiferromagnetic
interlayer coupling. The system exhibits Z$_{2}$ topological phase, protected
by pseudo-time-reversal symmetry (PTRS). An easy-plane anisotropy term breaks
PTRS and destroys the topological phase. Nevertheless, it respects a magnetic
two-fold rotational symmetry which protects a second-order topological phase
with corner modes in bilayer and hinge modes along stacking direction.
Moreover, an introduced staggered interlayer coupling establishes a
Z$_{2}$$\times$Z topology, giving rise to gapped topological surface modes
carrying non-zero Chern numbers. Consequently, chiral hinge modes propagate
along the horizontal hinges in a cuboid geometry and are robust against
disorders. Our work bridges the higher-order topology and magnons in van der
Waals platforms, and could be used for constructing topological magnonic
devices.
