The electronic structure and dispersion of optical constants of the Ba4CuGa5S12 and Ba4CuGa5Se12 compounds were calculated by the first-principles full-potential linearized augmented plane wave (FPLAPW) method. We employed the local density approximation (LDA), generalized gradient approximation (GGA) and Engel–Vosko GGA (EVGGA) to calculate the electronic structures, Fermi surface, thermoelectric, chemical bonding and dispersion of optical constants of these compounds. By investigating the influence of replacing S by Se, it has been found that the charge density around ‘Ga’ is greater in Ba4CuGa5Se12 than Ba4CuGa5S12. Fermi surface of Ba4CuGa5S12 consists of an electronic sheet only because there is no empty region while Ba4CuGa5Se12 contains both holes and electronic sheets because this compound contains both empty and shaded region. As we replace S by Se the heights of the peaks decreases as a results the reflectivity also decreases. It is noticed that the reflectivity is over 68% (60%) for Ba4CuGa5S12 (Ba4CuGa5Se12) compounds within the energy range studied. This implies that the material will serve as a good reflector. By replacing S by Se the figure of merit values increases from 0.97 to 1.0, which shows the good thermoelectric behavior of both compounds.