The density of states, electronic structure, optical and elastic properties of LiGaX2 (X=S, Se, Te) are investigated by the first-principles plane-wave pseudopotential density functional theory within the generalized gradient approximation (GGA). The results show that the band gaps of LiGaX2 (X=S, Se, Te) are 4.146 eV, 3.301 eV and 2.306 eV, respectively. It can be confirmed that the valence bands are mainly composed of X-np or Ga-4p states. The complex dielectric functions, reflectivity, index of refraction and elastic property are precisely calculated by band structure and density of states. The obtained results are in agreement with the available experimental data.