In this paper we are concerned with plane wave discretizations of nonhomogeneous and anisotropic time-harmonic Maxwell's equations. Combined with local spectral element method, we design a plane wave discontinuous Galerkin method for the discretization of such three dimensional nonhomogeneous and anisotropic Maxwell's equations. The error estimates of the approximation solutions generated by the proposed discretization method are derived in one special case of the TE mode scattering. In the error estimates, some dependence of the error bounds on the condition number of the anisotropic matrix is explicitly given. Numerical results indicate that the resulting approximate solutions generated by the new method possess high accuracy and verify the validity of the theoretical results.