Based on that the potential functions and medium parameter are irrelative and expanding the electric fields inside & outside the anisotropic medium target into series, the nthorder expressions both of scattering field from an anisotropic medium target and its inner elelctric field are developed. The transformation of the dielectric constant tensor is presented. When a plane electromagnetic wave incident in arbitrary direction, a general relation between the unit vector in propagation and that in polarization is expressed. Taking the magnetized cold plasma as an example, the first order scattering is developed and the error induced by the second order field is evaluated. In the THz wave band and optical wave band, the obtained result is simulated. Simulation results show that the differential scattering change sensitively with operating frequency and the polarization etc.; the nondiagonal elements of the tensor have no influence on the scattering; when the wave length and the size of the target are given, the simulations are correct in THz wave band and validate in other wave band.