Measurements of X-ray photoelectron core-level and valence-band spectra for pristine and irradiated with Ar+ ions surfaces of LiGa0.5In0.5Se2 single crystal, novel nonlinear optical mid-IR selenide grown by a modified vertical Bridgman-Stockbarger technique, are reported. Electronic structure of LiGa0.5In0.5Se2 is elucidated from theoretical and experimental points of view. Notably, total and partial densities of states (DOSs) of the LiGa0.5In0.5Se2 compound are calculated based on density functional theory (DFT) using the augmented plane wave + local orbitals (APW + lo) method. In accordance with the DFT calculations, the principal contributors to the valence band are the Se 4p states, making the main input at the top and in the upper part of the band, while its bottom is dominated by contributions of the valence s states associated with Ga and In atoms. The theoretical total DOS curve peculiarities are found to be in excellent agreement with the shape of the X-ray photoelectron valence-band spectrum of the LiGa0.5In0.5Se2 single crystal. The bottom of the conduction band of LiGa0.5In0.5Se2 is formed mainly by contributions of the unoccupied Ga 4s and In 5s states in almost equal proportion, with somewhat smaller contributions of the unoccupied Se 4p states as well. Our calculations indicate that the LiGa0.5In0.5Se2 compound is a direct gap semiconductor. The principal optical constants of LiGa0.5In0.5Se2 are calculated in the present work.