  We prove the consistency of the G\"{o}del metric with the Horava-Lifshitz
gravity whose action involves terms with z=1, z=2 and z=3. We show that, for
different relations between the parameters of the theory, this consistency is
achieved for different classes of matter, in particular, for the small
cosmological constant it is achieved only for the exotic matter, that is,
ghosts or phantom matter.
