Two isomers of 1,2,4-triazol-5-one: 1,2,4-trihydro-1,2,4- triazol-5-one (Ⅰ) and 2,3,4-trihydro-1,2,4-triazol-5-one(Ⅱ) were fully optimized by HF/6-31G^** and B3LYP/6-31G^**. The total energy calculation was also performed by MP2/6-31G^**//B3LYP/6-31G^**. The geometry,electron structure,net charges of atoms and vibration spectroscopic properties were calculated. The stabilities of the two compounds were analyzed and compound Ⅰwas more stable than Ⅱ which is consistent with the experimental results.