The numerical simulations have been conducted to clarify the effects of the turbulence in the liquid on the onset of protrusions on liquid jet surface. The turbulences in the liquid jet were simulated by the Rankin vortices. The liquid jet surface was tracked numerically by the VOF method. By the numerical simulations, the protrusions on the liquid jet surface are induced by the vortices in the liquid of which the rotation direction is that decelerates the jet surface. Instead of the distance between vortices, the displacement of the liquid jet surface increases linearly in time at almost the same growth rate. In the initial region where the displacement of the liquid jet surface is amplified, as the major semiaxis-to-minor semiaxis ratio of the ellipsoidal vortex increases the growth rate of the displacement increases. The initial growth rate of the wave on a liquid jet surface is almost proportional to the vortex intensity.