•Two bubbles coalescence under ultrasound irradiation is simulated.•Initial phase is important in the ultrasound acceleration of the coalescence.•Film formation during the coalescence between two bubbles is investigated.•Relationship between drainage time and bubble initial distance is investigated. The coalescence of two bubbles under ultrasound irradiation is numerically investigated. The results indicate that ultrasound may accelerate the coalescence process, depending on the initial phase. The time-averaged nonzero Bjerknes force promotes bubble coalescence by dragging bubbles to nodes or antinodes, depending on their size. At the beginning of the coalescence process, a film forms between the two bubbles. The film drainage time first increases then decreases as a function of initial distance. This study contributes to an understanding of the effects of ultrasound on bubble coalescence.