  By making use of the weak gravitational field approximation, we obtain a
linearized solution of the gravitational vacuum field equation in an
anisotropic spacetime. The plane-wave solution and dispersion relation of
gravitational wave is presented explicitly. There is possibility that the speed
of gravitational wave is larger than the speed of light and the casuality still
holds. We show that the energy-momentum of gravitational wave in the
ansiotropic spacetime is still well defined and conserved.
