The first-principle method was used to investigate the elastic anisotropy and thermodynamic properties of Tantalum borides (B–Ta) compounds. The anisotropic indexes, the 3D surface constructions and 2D projections of Young's modulus indicate that B–Ta compounds are anisotropic. The order of elastic anisotropy is B2Ta > BTa2> BTa > B2Ta3>B4Ta3>B6Ta5. Dynamical and thermodynamic properties indicate that B–Ta compounds can keep the dynamical stability at ground state and high temperature. The calculated Debye temperatures of the various B–Ta compounds predict the good mechanical strength at elevated temperatures.