An analytical solution of Gaussian beam scattering by a conducting circular cylinder coated with an anisotropic material is formulated in terms of the wave functions for anisotropic media. This solution is formally similar to the solution of Gaussian beam scattering by a conducting elliptical cylinder with an isotropic dielectric coating. In the anisotropic dielectric coating and in the exterior free space region, the fields are expanded by the newly developed wave functions for anisotropic media and the well-known wave functions for isotropic media, respectively. Numerical results are presented for the reference purpose. The effects of the spot size and the location of the waist of the beam, and the electrical size of the anisotropic-coated conducting circular cylinder on the scattered field are discussed.