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In this paper, negative refraction in the two-dimensional (2D) hexagonal lattices annular photonic crystal (APC) was theoretically studied. The annular photonic crystal was obtained by introduced circular-air-hole in the core of the Si-rod. The properties of the designed APC, such as photonic band structure, equal-frequency contours (EFCs) and the electric field distribution are analyzed by using Plane Wave Expansion (PWE) method and Finite-Difference Time-Domain (FDTD) method. Numerical simulations show that negative refraction and super-lens imaging can be realized in the designed annular photonic crystal for the normalized frequency from 0.2983(2πc/a) to 0.347(2πc/a). And it was also found that the resolution decreases linearly with the increasing of the inner radius.