The electronic structure, optical properties and crystal structure of the dilute bismide InSb1−xBix alloys with (0 ≤ x ≤ 0.125) have been studied using the DFT FP − LAPW method within the novel TB-mBJ and WC-GGA models. The lattice constant increases quasi-linearly in InSb1−xBix for small Bi contents. Based on calculations of the formation energy, we demonstrated the thermodynamic stability of the alloys. The small content of Bi into InSb1−xBix results in a large bandgap narrowing by ∼ 264 meV up to a composition of 0.125 covering the mid- and long wavelength IR ∼ 3.4–12.5 μm spectral range. From DOS analysis, a bandgap reduction in the InSb1-xBix can be explained by both upward movement of the valence band (VB) induced by the resonance interaction of Bi-6p states at the top of VB and the downward moves of In-s and Sb/Bi-p states at the conduction band (CB). A semiconductor-semimetal transition in InSb1−xBix at × ∼ 0.137 was expected. The optical properties in terms of dielectric functions (ε1, ε2), refractive index n, extinction coefficient k, reflectivity R and the absorption coefficient α were calculated for photon energies of 0–8 eV and compared to experimental data. The sharp energy structures appear in various optical spectra associated with interband transitions from occupied In-s, Sb-p and Bi-p orbitals located at VBmax to unoccupied In-s/p, Sb-p and Bi-p states located at CBmin. Good absorbance in the ultraviolet range was observed, which is useful for solar cells design. InSb1−xBix/InSb bismide alloy is an attractive candidate for realizing highly efficient light-emitting sources and photodetectors operating in the long-wavelength infrared spectral range (λLWIR ≥ 8 μm).