  We carried out inelastic neutron scattering experiments on a buckled
honeycomb lattice antiferromagnet Ba$_{2}$NiTeO$_{6}$ exhibiting a stripe
structure at a low temperature. Magnetic excitations are observed in the energy
range of $\hbar \omega \lesssim 10$ meV having an anisotropy gap of 2 meV at 2
K. We perform spin-wave calculations to identify the spin model. The obtained
microscopic parameters are consistent with the location of the stripe structure
in the classical phase diagram. Furthermore, the Weiss temperature
independently estimated from a bulk magnetic susceptibility is consistent with
the microscopic parameters. The results reveal that a competition between the
NN and NNN interactions that together with a relatively large single ion
magnetic anisotropy stabilize the stripe magnetic structure.
