The objective of this paper is the examination of structural, electronic, and optical properties of binary AlSb, AlN, and their novel ternary AlNxSb1−x alloys (x = 0.25, 0.5, and 0.75), within the full-potential linearized augmented plane wave method based on the density functional theory as implemented in the WIEN2K code. The computed negative formation energies of AlNxSb1−x alloys prove that these compounds are thermodynamically stable. The structural parameters are calculated using the generalized gradient approximation GGA–PBEsol, such as the lattice parameters, bulk modulus, and pressure derivatives, which are in good accordance with both theoretical and experimental data for binary compounds. However, for the ternary alloys, our results are considered as a first prediction. The lattice constants and the bulk modulus are compared with Vegard’s law and the linear concentration dependence. The Tran–Blaha-modified Becke–Johnson approach “TB–mBJ” is employed to determine the electronic and optical properties; the results demonstrate that the binary compounds have indirect band gaps (Γ–X), whereas the ternary AlNxSb1−x alloys exhibit direct band gaps (Γ–Γ) semiconductors, with values of 0.472, 0.915, and 1.962 eV for AlN0.25Sb0.75, AlN0.5Sb0.5, and AlN0.75Sb0.25, respectively. The obtained results are reported, discussed, and compared with previous and the experimental data.