Abstract The crystal structure, electronic and optical properties of double perovskite Sr 2 MgMoO 6 have been calculated by using the full-potential linear augmented plane wave (FP-LAPW) method. The band structure and density of states (DOS) were carried out by the modified Becke–Johnson (mBJ) exchange potential approximation based on the density functional theory (DFT). The calculated band structure shows a direct band gap ( Γ – Γ ) of 2.663 eV for Sr 2 MgMoO 6 . The compound Sr 2 MgMoO 6 has a triclinic structure with the space group I-1 , the lattice parameters a =5.5666 A, b =5.5661 A and c =7.9191 A, which are used in our calculations. The optical parameters, like dielectric constant, refractive index, reflectivity and energy loss function were also calculated and analyzed. This work provides the first quantitative theoretical prediction of the optical properties and electronic structure for the triclinic phase of Sr 2 MgMoO 6 .