To investigate the energy bands structure of α-Hg3S2Cl2, first-principles calculations were performed within the density functional theory (DFT) formalism using the SIESTA software package. Using the local density approximation the atomic positions are relaxed so as to minimize the forces acting on the atoms. The analysis of band energy dispersion shows that the VBM and CBM are located at Г symmetry point, resulting in a direct energy band gap of 3.198 eV. It is established that the nature of interatomic interactions has complex character and includes covalent and ionic parts. The inclusion of spin-orbit coupling does not strongly modifies the structure of energy bands.