This paper aims at designing a 2D photonic crystal (PC) with negative refractive index close to -1. Plane wave expansion method (PWEM) is used to obtain the band diagram and its equal-frequency surface (EFS). And the finite difference time domain (FDTD) simulation method is also used to analyze the equivalent refractive index of the PC. The results show the equivalent refractive index of the PC close to -1 within a certain frequency band. A super-lens is formed by this photonic crystal, which can form a non-near-field image. Moreover, the super-lens has the capability of sub-wavelength imaging with its effective index close to -1.