We report on results of first principle calculations on La₂GaN₃. Equilibrium lattice parameters a, c, β and V were calculated, the results are in good agreement with experimental data. Elastic constants C_ij for single crystal;  the deduced parameters bulk modulus B, shear modulus G, Young modulus E and the compressibility coefficients χ_a, χ_c, χ_v for polycrystalline aggregate were also presented.  Bonding nature and bonds strength were discussed based on two points of view. Firstly, from the pressure effect on the structural parameters and the relative change of the bonds length. Secondly, from the electronic aspect based on the partial densities of states and the electronic charge distribution. La₂GaN₃ has an indirect band gap energy of 1.3 eV which decreases with increasing pressure. Thermodynamic properties such as Debye temperature θ_D, heat capacities (C_v and C_p) and expansion coefficient α_V were investigated based on the quasi-harmonic Debye model. Dielectric optical function, refractive index and absorption coefficient suggest that this compound is promising candidate for photovoltaic applications due to its high absorption of solar radiation in the visible range .