Based on newly improved optical parameters of the excellent biaxial crystal LiGaS 2 , its phasematching upon second harmonic generation and general parametric processes are investigated. In particular, the issue of optimal phase-matching is solved by a computation on figureof-merit (FM). It is found that the effective fundamental wavelength of second harmonic generation entirely covers the 3-5 µm atmosphere window and mid-IR signals of 2-12 µm can be generated by suitable parametric processes. Analysis of the FM and dispersion verifies a quite effective type II parametric process: from a pump in the range of 0.8-1.0 µm to an ultrashort pulse generation at 6-12 µm and also suggests a type I pump at 1.7-1.9 µm for 3-5 µm pulse generation. The computation definitely renders an optimal phase-matching in the XY principal plane for type II configuration, or in a special direction for type I case, far away from the commonly used XZ principal plane.