According to the Sellmeier dispersion equation and law of energy conservation and momentum conservation,the tuning characteristics,conversion efficiency,permitted parametric and walk-off effect of ZGP-DFG have been obtained using numerical simulation in type-Ⅰ and type-Ⅱ phase-matched. The ranges of angle tuning were 51°-89° in type-Ⅰ,and 58°-88° in type-Ⅱ. The corresponding ranges of wavelength were 3.1-12 μm and 6.2-11.5 μm,respectively. In addition,the corresponding characteristics of AgGaS2 (AGS) and AgGaSe2 (AGSe) were compared with ZGP,and the conclusion was the walk-off effect of ZGP-DFG was small,and the conversion efficiency of ZGP-DFG was the highest among the three crystals. In summary,ZGP was a better crystal to produce the mid-infrared laser.