Progressive meshes will meet the requirements of generating multi-resolutions meshes of a 3D model. Among the methods available, more than 4 adjacent vertices are associated to simplify a vertex. Moreover, meshes are represented by vertex-face list structure, which has bad experience in searching neighbor information. In this paper, √3 subdivision method is introduced to predict the vertex to be simplified, and only 3 adjacent vertices are considered. In the meantime, a half-edge map is constructed to replace vertex-face list so as to speed up the neighbor information search. Experimental results show that the method proposed in this paper improves both time efficiency and space efficiency of generating progressive meshes.