First-principles study of LiGa Li₂S, GaS, Ga₂S₃ and LiGaS₂ thermodynamic functions in Li-Ga-S system was performed by using plane-wave pseudopotential method. All possible chemical reactions were analyzed. It was found that the goal product LiGaS₂ comes from four chemical reactions. Free energy change of direct synthesis from elements is high. Free energy change of synthesis from Li₂S and Ga₂S₃ decreases with increasing temperature, but Ga₂S₃ is difficult to be obtained. These two reactions can not occur in this system. The remaining reactions by LiGa and S method and Li₂S and GaS method can occur due to their low free energy changes. Free energy changes generating Li₂S, GaS and LiGa are low.