  The magnetic excitations in CoPS$_3$, a two-dimensional van der Waals (vdW)
antiferromagnet with spin $S=3/2$ on a honeycomb lattice, has been measured
using powder inelastic neutron scattering. Clear dispersive spin waves are
observed with a large spin gap of ~13 meV. The magnon spectra were fitted using
an $XXZ$-type $J_1-J_2-J_3$ Heisenberg Hamiltonian with a single-ion anisotropy
assuming no magnetic exchange between the honeycomb layers. The best-fit
parameters show ferromagnetic exchange $J_1=-2.08$ meV and $J_2=-0.26$ meV for
the nearest and second-nearest neighbors and a sizeable antiferromagnetic
exchange $J_3=4.21$ meV for the third-nearest neighbor with the strong
easy-axis anisotropy $K=-2.06$ meV. The suitable fitting could only be achieved
by the anisotropic $XXZ$-type Hamiltonian, in which the exchange interaction
for the out-of-plane component is smaller than that for the in-plane one by a
ratio $\alpha=J_z/J_x=0.6$. Moreover, the absence of spin-orbit exciton around
30 meV indicates that Co$^{2+}$ ions in CoPS$_3$ have a $S=3/2$ state rather
than a spin-orbital entangled $J_\rm{eff}=1/2$ ground state. Our result
directly shows that CoPS$_3$ is an experimental realization of the $XXZ$ model
with a honeycomb lattice in 2D vdW magnets.
