Based on the principle that both scalar potential and vector potential are independent of the dielectric tensor, by using the relation between electric dipoles and their potentials, the analytical expression of scattering field for the anisotropic medium target is developed. The transformation of dielectric tensor is researched. The expression of a tensor in spherical coordinate system is presented in detail. The electric fields inside and outside the target are expanded in series, and then the primary scattering field from the anisotropic gypsum cone is presented. The theoretical result coincides with those in literatures and its validity is tested. When the wavelength is near to the size of the nanoparticle, some simulations are carried out, the result shows that the scattering of anisotropic cones has the characteristic of dipole radiation. The method used is simple and universal. The result has provided a theory for studying the laser scattering from a complex anisotropic target.