In this paper, the fully optimized molecular geometries and electronic structures of six 1,2,3- and 1,2,4-triazoles were calculated using density functional theory B3LYP/6-311G** method. The salvation energies were obtained by SCRF in THF. The results show that the total energies of F are the lowest both in gas and liquid phases, and the order of thermodynamic stabilities of the title compounds is F＞D＞C＞B＞E＞A. Their frontier orbital energy gaps and electron delocalization also support that F is the most stable. All the computed conclusions are in good agreement with the experiments. Vibrational frequencies of the title compounds were computed. The thermodynamic properties and their temperature curves of six compounds were obtained by using the statistical thermodynamic method with the temperature ranging from 200 to 1000 K.