We theoretically studied a left-hand structure based on a two-dimensional (2D) photonic crystal (PC) with a negative refractive index. The propagation of electromagnetic waves in the proposed PC structure is investigated through dispersion characteristic analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction, and the corresponding effective refractive indices along all directions are almost same and close to the ideal value of -1. A flat lens formed from such a PC has been designed and its imaging properties have been investigated systematically.