A level-set (LS) method is presented for vapor bubble motion in acoustic fields. The effects of compressibility and phase change are implemented using the ghost fluid method and the semi-implicit pressure correction method. The present numerical method is validated through computations of one-dimensional compressible single-phase and two-phase flows. Computations are performed for bubble growth in acoustic droplet vaporization (ADV) by including two LS functions for the liquid-vapor and liquid-liquid interfaces. The effects of acoustic wave and ambinet temperature on the vaporization of a volatile droplet immersed liquid water are investigated.