Density functional theory (DFT) calculations within the concept of the MBJ+U+SO (modified Becke-Johnson potential + U + spin orbit) approach were performed for a Tl4HgBr6 single crystal for the first time assuming weak noncentrosymmetry (space group P4nc). Excellent agreement was achieved between the calculated and experimental band-gap-energy magnitudes as well as the density of electronic states measured by the X-ray photoelectron spectroscopy method. It is a very principal result because usually the DFT calculations underestimate the energy-gap values. In the present study, we carry out calculations of the optical properties (absorption coefficient, real and imaginary parts of the dielectric function, electron energy-loss spectrum, refractive index, extinction coefficient, and optical reflectivity dispersions). It has been established that the principal origin of the observed weak acentricity is determined by delocalized band states at the top of the valence band originating from the p states of the Br atoms.