Cavitation bubbles always exist in the diesel jet leaving the nozzle and in the diesel droplets breaking up from the jet as a result of supercavitation of the diesel within the injection nozzle, and it can increase the instability of jet and droplets in part due to the two-phase mixture, while the mechanism of this effect is still unclear. Growth and collapse of spherically symmetric bubble within the diesel droplet has been then simulated numerically based on the volume of fluid (VOF) method. The numerical results show that the process of bubble growth is divided into three stages, including surface tension controlled domain, comprehensive competition controlled domain with the surface tension, the inertial force and the viscous force, and inertial force controlled domain. In addition, the bubble collapse within a droplet consists of multiple collapse and rebound stages, similar to the vibration process of a damping spring oscillator. According to the variation of bubble radius with time at the end of each cycle, the process of bubble collapse can be divided into fast, slow and stable stages.