The single supersonic free jet discharging from a nozzle or an orifice has been often employed in various industrial processes. A number of studies have been done on the major features (Mach disk, barrel shock wave and the jet boundary configuration) of the supersonic jets. In the present study, numerical computations were performed to investigate the effect of initial degree of supersaturation of moist air at reservoir condition on under-expanded jet structures and the total pressure loss behind the Mach disk. From these studies, it was found that the position of Mach disk in the under-expanded moist air jets was almost the same as that in dry air jets. However, the diameter of Mach disk increased slightly with an increase in the initial degree of supersaturation of moist air. Furthermore, the total pressure loss behind the Mach disk of moist air jet changed largely in comparison to that of dry air jet.