ABSTRACT Fast radio bursts (FRBs) are newly discovered radio transient sources. Their high dispersion measures indicate an extragalactic origin. However, due to the lack of observational data in other wavelengths, their progenitors still remain unclear. Here we suggest that the collisions between neutron stars (NSs) and asteroids/comets are promising mechanisms for FRBs. During the impact process, a hot plasma fireball forms after the material of the small body penetrates into the NS surface. The ionized matter inside the fireball then expands along the magnetic field lines. Coherent radiation from the thin shell at the top of the fireball will account for the observed FRBs. Our scenario can reasonably explain the main features of FRBs, such as their durations, luminosities, and the event rate. We argue that for a single NS, FRBs are not likely to happen repeatedly in a forseeable timespan since such impacts are of low probability. We predict that faint remnant X-ray emissions should be associated with FRBs, but it may be too faint to be detected by detectors at work.