Abstract: The structural, electronic, and nonlinear optical properties of a γ-TeO₂ crystal have been studied using nonempiric quantum-mechanical calculations. The electron localization on the 5d orbital is taken into account using the Hubbard corrections to the density functional (the LDA + U approximation). The use of this approach enables a fairly correct reproducibility of the experimental structural parameters. The electronic structure is studied using the G₀W₀ quasi-particle approximation that recommended itself as one of most exact methods of calculating the band structure. The γ-TeO₂ crystal is found to be a wide bandgap semiconductor with indirect optical transition. Using the maximally localized Wannier functions, the chemical binding in this oxide is analyzed and it is shown that valent electrons of oxygen atoms are in sp3 hybridization, and the tellurium atom valence is four.