The entrapment of bubble during droplet impact on solid surfaces was studied by using a phase-field lattice Boltzmann model (LBM). Numerous three-dimensional simulations were performed and several types of entrapment were found under specific impact conditions. Some cases are similar to previous studies, whereas others are reported for the first time. Dissections of the entrapment processes were carried out, and detailed analyses of the flow fields and interface motions were provided at selected moments for certain cases. The effects of the Reynolds number, the Weber number and the surface wettability were analyzed based on the observation. Besides, some computational issues of phase-field simulations were discussed for the present problem. Finally, the impact condition to prevent entrapment was preliminarily estimated in terms of the Ohnesorge number upon examination of numerous simulations. Copyright © 2009 John Wiley & Sons, Ltd.