By using the Linearized Muffin-Tin Orbital Method, the surface electronic structure of several "stable Ａｇ（１１１） surfaces" obtained by different methods were systematically studied and contrasted, the different surface electronic character of the different relaxation surfaces were presented and discussed. According to the surface energy, the most stable Ａｇ（１１１） surface was single layer inward relaxed surface, and the local electronic densities of states of this king of structure were presented and discussed. The local electronic dendities of states of ideal clean Ａｇ（00１） surface were also studied, and the results that the Ａｇ（00１） surface were also presented. the Ａｇ（００１） surface is more stable than Ａｇ（１１１）.