The influence of Sb-doping in the Bi-based double perovskite \({\text{B}\text{a}}_{2}{\text{T}\text{b}\text{B}\text{i}}_{1-\text{x}}{\text{S}\text{b}}_{\text{x}}{\text{O}}_{6}(\text{x}=0.0, 0.5)\) to provide a structural and electronic basis for comprehending various physical properties in an atomistic level. Using first-principles calculations based on density functional theory (DFT) implemented via the VASP code. For the first time we study the comprehensive analysis of the structural, elastic, mechanical, electronic, and thermodynamic properties of undoped and Sb-doped \({\text{B}\text{a}}_{2}\text{T}\text{b}\text{B}\text{i}{\text{O}}_{6}\) double perovskite (cubic and monoclinic phases). Changing the spatial group structure and lattice constant of \({\text{B}\text{a}}_{2}\text{T}\text{b}\text{B}\text{i}{\text{O}}_{6}\) by doping causes a shift in the Brillouin zone, which in turn modifies the band structure and band gap value. The overall DOS profiles of both doped and undoped phases were identical to those of the undoped sample, however the conduction and valance bands for both doped compositions were slightly pushed nearer the fermi level. The elastic constants verified the ductility of the solids and ensured the mechanical stability of both phases. Before and after doping, the monoclinic phase is ductile while the cubic phase is brittle. This study reveals that both the phases of \({\text{B}\text{a}}_{2}{\text{T}\text{b}\text{B}\text{i}}_{1-\text{x}}{\text{S}\text{b}}_{\text{x}}{\text{O}}_{6}\) are mechanically stable, ductile, and machinable than\({\text{B}\text{a}}_{2}\text{T}\text{b}\text{B}\text{i}{\text{O}}_{6}\). Although both phases were anisotropic, the Sb-doped monoclinic phase showed higher anisotropy than the cubic phase. Vickers hardness shows that monoclinic \({\text{B}\text{a}}_{2}{\text{T}\text{b}\text{B}\text{i}}_{1-\text{x}}{\text{S}\text{b}}_{\text{x}}{\text{O}}_{6}(\text{x}=0.0, 0.5)\) phase is harder than cubic \({\text{B}\text{a}}_{2}{\text{T}\text{b}\text{B}\text{i}}_{1-\text{x}}{\text{S}\text{b}}_{\text{x}}{\text{O}}_{6}(\text{x}=0.0, 0.5)\) phases. Moreover, the thermodynamic properties of all the studied compounds are estimated by using the elastic constant data. The cubic and monoclinic phases of\({\text{B}\text{a}}_{2}{\text{T}\text{b}\text{B}\text{i}}_{0.5}{\text{S}\text{b}}_{0.5}{\text{O}}_{6}\)have Debye temperatures of 248.48 and 240.75 K, respectively. After doping, the melting temperature of cubic phase (1529.21 K) rises greater than that of monoclinic phase (1386.87 K). Doping can improve a material’s stability by reducing its thermal expansion coefficient. Both the doped phases can be employed as a thermal barrier coating (TBC). The doped cubic phase in high-efficiency conversion applications like solar cells and other optoelectronic devices.