Neutron inelastic scattering has been used to measure the magnetic excitations in powdered NiPS₃, a quasi-two-dimensional antiferromagnet with spin S = 1 on a honeycomb lattice. The spectra show clear, dispersive magnons with a ∼7 meV gap at the Brillouin zone center. The data were fitted using a Heisenberg Hamiltonian with a single-ion anisotropy assuming no magnetic exchange between the honeycomb planes. Magnetic exchange interactions up to the third intraplanar nearest neighbor were required. The fits show robustly that NiPS₃ has an easy-axis anisotropy with Δ = 0.3 meV and that the third nearest neighbor has a strong antiferromagnetic exchange of J₃ = -6.90 meV. The data can be fitted reasonably well with either J₁ < 0 or J₁ > 0, however, the best quantitative agreement with high-resolution data indicates that the nearest-neighbor interaction is ferromagnetic with J₁ = 1.9 meV and that the second nearest-neighbor exchange is small and antiferromagnetic with J₂ = -0.1 meV. The dispersion has a minimum in the Brillouin zone corner that is slightly larger than that at the Brillouin zone center, indicating that the magnetic structure of NiPS₃ is close to being unstable.