Using the plane wave expansion method, we have calculated, for both E and H polarizations, the band structure of 2D anisotropic photonic crystals with honeycomb lattice composed of anisotropic tellurium (Te) rods embedded in air background. The two rods in the unit cell are chosen square and circular in shape. Here, from a practical point of view, in order to obtain maximum band gaps, we have also studied the band structure as a function of size of rods.