We propose a two-dimensional (2D) annular photonic crystal (APC) with dual equi-frequency contours (EFCs) in one band. The refractive behaviors of a Gaussian beam incident from air to the APC are analyzed by the EFC analysis and finite-difference time-domain (FDTD) method. The results show the positive-negative birefraction phenomenon for the transverse magnetic (TM) polarization in the same band occurs at the interface between air and the APC, and the surface termination of the APC has a large effect on the strength of the negatively refracted beam.