An all electron full potential linearized augmented plane wave method has been applied for a theoretical study of the band structure, density of states, and electron charge density of a noncentrosymmetric chalcopyrite compound HgGa2S4 using three different approximations for the exchange cot-relation potential. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at F resulting, in a direct energy gap of about 2.0, 2.2, and 2.8 eV for local density approximation (LDA), generalized gradient approximation (GGA), and Engel-Vosko (EVGGA) compared to the experimental value of 2.84 eV. We notice that EVGGA shows excellent agreement with the experimental data. This agreement is attributed to the fact that the Engel-Vosko GGA formalism optimizes the corresponding potential for band structure calculations. We make a detailed comparison of the density of states deduced from the X-ray photoelectron spectra with our calculations. We find that there is a strong covalent bond between the Hg and S atoms and Ga and S atoms. The Hg-Hg, Ga-Ga, and S-S bonds are found to be weaker than the Hg-S and Ga-S bonds showing that a covalent bond exists between Hg and S atoms and Ga and S atoms.