The tautomerizations of polyazido-azine(ring-closure reaction) for 3,6-diazido-1,2,4,5-tetrazine(DiAT) and 2,4,6-triazido-1,3,5-triazine(TAT) were investigated by density functional theory. All of the stationary points(reactants,transition states and products) on the reaction paths were optimized at the B3LYP/6-311G^** level. The total energies were obtained after zero-point vibrational energy correction. Enthalpies of formation were derived via the designed isodesmic reactions. The changes of energies,geometries and enthalpies of formation in the tautomerization were analyzed. The cyclization of 3,6-diazido-1,2,4,5-tetrazine processes by two steps with energy barriers of 100.5 and 117.4 kJ·mol^-1,respectively,and the cyclization of 2,4,6-triazido-1,3,5-triazine by three steps with energy barriers of 101.8,99.7 and 108.7 kJ·mol^-1. The enthalpies of formation increase in the process of cyclizations. The ring-closure reaction of TAT is thermodynamically more unfavorable in comparison to that of DiAT. The solvent effect of dimethyl sulfoxide on the tautomerization was evaluated with the self-consistent reaction field (SCRF) method.