Using a mid-infrared CO₂ laser in terahertz difference frequency generation (THz-DFG) is an effective method for improving conversion efficiency and output power. According to the three-wave interaction of difference frequency, the AgGaS₂ crystal is analyzed theoretically. The angle tunable curves of difference-frequency-generated THz wave under both oeo-type and oee-type phase matching conditions are simulated numerically. The walk-off angle and acceptable parameter of light wave in the crystal are calculated. In addition, the effective nonlinear coefficient and theoretical power conversion efficiency of the crystal are taken into account. The research result shows that the AgGaS₂ crystal is suitable for widely tunable THz-DFG with a CO₂ laser.