The accuracy of DEMs is the key issue for its quality and various applications. Theoretically, terrain morphology is the basis to derive the topographic information. Therefore, to establish the methodology of DEM's morphologic accuracy can promote the high-quality DEM productions and their widespread applications. Focusing on the cognition of the local slope concave-convex property, this paper analyses the influences of grid point locations and grid cell sizes on this morphological property. As such, this paper arms to further improve and develop the theory and method of DEM quality. At first, this paper introduces the basic concept of terrain morphology accuracy represented by the gridded DEM, consisting of elevation sampling accuracy and elevation relation accuracy of local points, local slope morphology accuracy, regional terrain relation accuracy and global terrain structure accuracy. Herein, the local slope morphology accuracy can be represented by the local slope concave-convex property, including three categories of flat slope, concave slope and convex slope. To quantify the concave-convex property, the error metric is defined using the multi-scale DEMs and several statistic indexes of the error metric are presented. At last, taking loess hill region as the study area and 5、10、15、25、…、155 m DEMs generated by the TIN-based method as the experimental dataset, the comparative method is applied to investigate the characteristics of the local slope concave-convex slope varied with the grid-point location and the grid cell size. The main conclusions of this research are reached as follows: (1) the morphology accuracy of DEMs must be considered in the production of high-quality DEMs. In this study, 10 m size (jumping rate is equal or lesser than 0.3%) is optimal threshold of the grid cell size for 1:50 000 DEMs. (2) When the DEM resolution is higher than the threshold, the DEM has almost the same concave-convex property with the real topography, followed by the less changes in the transition area between the positive and negative terrains. When the resolution of DEM is lower than the threshold, the local slope concave-convex property would have a significant uncertainty changed with the grid-point location and the DEM resolution.