We present results of electronic structure calculations on the N-related localized vibrational modes in the dilute nitride alloy GaSb1-xNx. By calculating the formation energies of various possible N incorporation modes in the alloy, we determine the most favorable N configurations, and we calculate their vibrational mode frequencies using density functional theory under the generalized gradient approximation to electron exchange and correlation, including the effects of the relativistic spin-orbit interactions. For a single N impurity, we find substitution on an Sb site, NSb, to be most favorable, and for a two-N-atom complex, we find the N-N split interstitial on an Sb site to be most favorable. For these defects, as well as, for comparison, defects comprising two N atoms on neighboring Sb sites and a N-Sb split interstitial on an Sb site, we find well-localized vibration modes (LVMs), which should be experimentally observable. The frequency of the triply degenerate LVM associated with NSb is determined to be 427.6 cm-1. Our results serve as a guide to future experimental studies to elucidate the incorporation of small concentrations of N in GaSb, which is known to lead to a reduction of the band gap and opens the possibility of using the material for long-wavelength applications.