Based on first-principles density functional theory the electronic structure, optical and lattice dynamical properties of infrared nonlinear optical crystal AgGaS₂ (AGS) are calculated with four different hybrid functional (PBE0, HSE03, HSE06, B3LYP) respectively. The results show that the theoretical results obtained by PBE0 method are in good agreement with the experimental values. The geometrical structure optimization results show that the theoretical lattice parameters of AGS are in good agreement with the experimental values. The electronic structure results show that AGS is a direct wide band gap nonlinear optical crystal, and the band gap obtained by PBE0 method is 2.66 eV, which is basically in good agreement with the experimental values. The calculation results of energy band structure and density of states show that the value band edge is mainly contributed by S-3p, Ag-4d and a small amount of Ga-4p orbital electrons, while the bottom of conduction band is mainly contributed by Ag-5 s, Ga-4 s, 4p and a small amount of S-3p orbital electrons. The orbital coupling between Ga and S atoms determines the optical properties of AGS. Ag atoms contribute little to the optical properties. Especially, the results show that the crystal material has strong absorption and reflection characteristics in the ultraviolet region and strong transmittance in the infrared region. The average static dielectric constant and average static refractive index are 1.887 and 2.14, respectively, and the static birefringence is 0.02. Based on the density functional theory of linear response, the phonon dispersion curve of AGS is calculated. The results show that AGS has no virtual frequency and its dynamic performance is relatively stable. Meanwhile, the optical mode frequency of the Γpoint in the center of Brillouin region is analyzed in detail. The above results show that AGS crystal material enjoys large nonlinear optical coefficient and suitable birefringence in a wide infrared band, and AGS is an important infrared nonlinear optical crystal material.