The displacement damage cross-section of the neutron -GaN interaction is calculated in the energy range from meV to GeV. Different calculation methods are used and discussed to estimate the modeling uncertainty. The Non-ionizing energy loss (NIEL) and the relative damage factors are also deduced. Differences with the neutron -Silicon interactions are presented and the impacts on the estimation of Total Non-Ionizing Dose (TNID) levels are evaluated as a function of neutron energy.