The numerical simulations have been performed to clarify the effects of the turbulence in the liquid on the deformation of liquid jet surface issued into the air flow. The turbulences in the liquid jet were simulated by the Rankin vortices, and the liquid jet surface was tracked numerically by the VOF (Volume Of Fluid) method. By the numerical simulations, the onset of the protrusions on the liquid jet surface is caused by the vortices in the liquid, and the surrounding air flow plays the important role for the amplification of the protrusions. The amplification rate of the trough displacement is proportinal to the air-to-liquid velocity ratio. At large imposed vortex intensity, the trough displacement increases with the vortex intensity. On the other hand, at small imposed vortex intensity, the amplification of the trough displacement is affected by other factors except vortex intensity.