Studies of the electronic structure and optical properties of the GdNiSb half-Heusler alloy have been performed. Calculations of the total and partial densities of electronic states were carried out on the basis of the GGA + U method, taking into account the correction for strong interactions in the f-electron system of gadolinium ions. By the method of spectral ellipsometry in the range of 0.078-5.64 eV, the dielectric functions of the alloy are investigated, their dispersion features are revealed. The anomalous behavior of optical conductivity in the infrared region of the spectrum for metals was found, confirming the presence of an energy gap at the Fermi level in the electronic spectrum, predicted in the calculation. A comparative analysis of the experimental and theoretical frequency dependences of optical conductivity is carried out, the features of interband light absorption are identified. The plasma frequency of conduction electrons is determined.