  Fast radio bursts (FRBs) are newly discovered radio transient sources. Their
high dispersion measures indicate an extragalactic origin. But due to the lack
of observational data in other wavelengths, their progenitors still remain
unclear. Here we suggest the collisions between neutron stars and
asteroids/comets as a promising mechanism for FRBs. During the impact process,
a hot plasma fireball will form after the material of the small body penetrates
into the neutron star surface. The ionized matter inside the fireball will then
expand 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 neutron star, FRBs
are not likely to happen repeatedly in a forseeable time span 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.
