In this study, the first-principles method was used to predict the vacancy ordered structures of ternary Hf-Ta-C system and the effect of vacancy on its mechanical properties. Crystal structure of (Hf, Ta)C_1-x under ambient pressure were predicted by first-principles evolutionary using USPEX software. This calculation found 5 stable and 3 metastable vacancy ordered structures which all share the rock-salt structure. Then, mechanical properties of (Hf, Ta)C_1-x vacancy ordered structures were calculated by the first-principles method, and change of mechanical properties with the concentration of vacancy was analyzed. They all showed high bulk modulus, shear modulus, elastic modulus, and Vickers hardness. Their moduli and hardness decreased with the increase of the concentration of vacancy at the same Hf/Ta ratio. Finally, their electronic density of states are calculated, revealing that their chemical bonding is a mixture of strong covalence and weak metallic. Data from this study are promising for understanding vacancy ordered structures, mechanical properties and applications of Hf-Ta-C system.