Using first-principles calculations with the generalized gradient approximation (GGA), the band structure of the new BxGa1-xSb ternary alloys is studied theoretically, and the impact of the born incorporation on the band structure of BxGa1-xSb is also investigated. The result shows that, when boron relative mole content is between 0 and 18.75%, the value of Γ1c-Γ15v band-gap energy is increasing monotonously by ～17.5 meV/%B with a small band-gap bowing parameter (2.23 eV), while the value of X1c-Γ15v band-gap energy is decreasing monotonously by ～12.8 meV/%B. When boron content x is below 10%, BxGa1-xSb is a direct band-gap alloy. In addition, the formation enthalpies of BxGa1-xSb alloys with born relative mole content at 6.25%, 12.5% and 18.75% are also calculated, respectively. The comparison between the calculated formation enthalpies of BxGa1-xAs and that of BxGa1-xSb indicates that the content of boron in BxGa1-xSb may be able to reach 7% relative mole.