A short wave was observed on the interface of liquid jet which was injected from the coaxial dual nozzle into a co-current gas stream. This wave promoted the breakup of liquid jet. To clarify the inception mechanism of the short wave, the internal instability of liquid jet flow was analyzed numerically. It was shown that the short wave was mainly due to the internal disturbance within liquid jet which rose from the internal instability. The effect of liquid injection velocity ratio, the diameter ratio of the coaxial dual nozzle and the liquid properties upon the instability were examined numerically. Finally, it was found that the breakup of the coaxial liquid jet could be controlled by appropriate adjustment of these parameters.