  We investigate the hypothetical process of gravitational Cherenkov radiation,
which may occur in modified gravity theories. We obtain a useful constraint on
a modified dispersion relation for propagating modes of gravitational waves,
which could be predicted as a consequence of violation of the Lorentz
invariance in modified theories of gravity. The constraint from gravitational
Cherenkov radiation and that from direct measurements of the gravitational
waves emitted by a compact binary system are complementary to each other.
