In this article, the structural, mechanical, electronic, optical, thermal, and thermodynamic properties of Ba2XSbO6 (X=P, As) double perovskite oxides were investigated by using first-principles calculations. The results show that the Goldsmith’s tolerance factor and octahedral factor of the two perovskites are in a stable range, the binding energy and formation energy are negative, and the elastic constants meet the Born-Huang stability criterion. These results suggest the stability of the two perovskite oxides. The mechanical property study indicates that Ba2XSbO6 (X=P, As) exhibits high bulk modulus and shear modulus. Poisson’s ratio (ν) and the elastic anisotropy index (A) suggest that they are anisotropic ductile materials. The electronic properties show that Ba2PSbO6 and Ba2AsSbO6 are indirect bandgap semiconductors with bandgap values of 2.130 eV and 1.596 eV, respectively. The optical properties show that Ba2XSbO6 (X=P, As) has excellent light absorption capacity in the range of 2.5–30 eV. Specifically, Ba2AsSbO6 has a higher absorption capacity for visible light compared to Ba2PSbO6. Thermodynamic properties show that the Debye temperature of the two perovskites is higher than 420 K, the melting points is higher than 1700 K, the minimum lattice thermal conductivities is close to 1, and the specific heat reaches the Dulong-Petit limit at about 700 K. This study shows that the double perovskite oxide Ba2XSbO6 (X=P, As) has important potential in the field of thermoelectricity and optoelectronics.