The under-expanded jet discharged from a nozzle or an orifice has been extensively employed in industrial applications and aerospace technologies. A number of studies have been made to investigate the under-expanded jet structures such as Mach disk, barrel shock wave, jet boundary configuration, etc. In the current study, a computational work is performed to investigate the effect of non-equilibrium condensation of moist air on the under-expanded jet, which is discharged from a sonic nozzle. The results obtained are compared with an available experimental data. It is found that non-equilibrium condensation of moist air alleviates the oscillations of the under-expanded jet, and can increase Mach disk diameter, without changing the location.