The HNCN^- has been used in various spectroscopic investigations to probe the HNCN radical. The focus of this study is to present ab initio calculations on the motion of the hydrogen atom around the NCN^- system. The CCSD(T) methodology with a cc-pVTZ basis set has been used to calculate the barrier height for isomerization. The various equilibrium geometries are also presented. These results are compared to the neutral species. The two stable structures for the anion belong to the C_2v and C_∞v point groups.