A method to realize absolute negative refraction index [EQUATION] with a two-dimensional (2D) photonic crystal is presented by introducing dielectric anisotropy in the photonic crystal material. The band structures of E-polarization mode and H-polarization mode can be adjusted by changing the parameters of materials. Thus the two modes with different polarizations have the same negative refraction index [EQUATION] for the same frequency. The results are demonstrated by numerical simulation based on the finite-difference time-domain (FDTD) method.