Recently in terrain rendeing, most researches introduce mipmap-based out-of-core methods for handling large sized DEM data which does not fit in main memory of general computer. However, mipmap-based LOD(level-of-detail) methods occur geometric errors which appear in data simplifying the higher LOD level. These geometric errors cause geometric popping effects where LOD level changes when viewpoint moves. In this paper, we propose vertex cohesion map for reducing geometric error. In preprocessing step, we generate vertex cohesion map, which is a texture that stores the vectors. By these vectors, each vertex will be cohered into the position in which the difference of gradient value is bigger than others. Therefore in terrain rendering, using vertex cohesion map can dramatically reduce the geometry popping effects rather than using mipmap.