Authors:Dai et alAbstract:Very recently, Spitler et al. and Scholz et al. reported their detections of 16 additional bright bursts in the direction of the fast radio burst (FRB) 121102. This repeating FRB is inconsistent with all of the catastrophic event models put forward previously for hypothetically non-repeating FRBs. Here, we propose a different model, in which highly magnetized pulsars travel through the asteroid belts of other stars. We show that a repeating FRB could originate from such a pulsar encountering a large number of asteroids in the belt. During each pulsar-asteroid impact, an electric field induced outside of the asteroid has such a large component parallel to the stellar magnetic field that electrons are torn off the asteroidal surface and accelerated to ultra-relativistic energies instantaneously. The subsequent movement of these electrons along magnetic field lines will cause coherent curvature radiation, which can account for all of the properties of an FRB. In addition, this model can self-consistently explain the typical duration, luminosity, and repetitive rate of the 17 bursts of FRB 121102. The predicted occurrence rate of repeating FRB sources may imply that our model would be testable in the next few years.