The global digital elevation model (DEM) is important for various scientific applications. With the recently released TanDEM-X 90-m DEM and AW3D30 version 2.2, the open global or near-global coverage DEM datasets have been further expanded. However, the quality of these DEMs has not yet been fully characterized, especially in the application for regional scale studies. In this study, we assess the quality of five freely available global DEM datasets (SRTM-1 DEM, SRTM-3 DEM, ASTER GDEM2, AW3D30 DEM and TanDEM-X 90-m DEM) and one 30-m resampled TanDEM-X DEM (hereafter called TDX30) over the south-central Chinese province of Hunan. Then, the newly-released high precision ICESat-2 (Ice, Cloud, and land Elevation Satellite-2) altimetry points are introduced to evaluate the accuracy of these DEMs. Results show that the SRTM1 DEM offers the best quality with a Root Mean Square Error (RMSE) of 8.0 m, and ASTER GDEM2 has the worst quality with the RMSE of 10.1 m. We also compared the vertical accuracies of these DEMs with respect to different terrain morphological characteristics (e.g., elevation, slope and aspect) and land cover types. It reveals that the DEM accuracy decreases when the terrain elevation and slope value increase, whereas no relationship was found between DEM error and terrain aspect. Furthermore, the results show that the accuracy increases as the land cover type changes from vegetated to non-vegetated. Overall, the SRTM1 DEM, with high spatial resolution and high vertical accuracy, is currently the most promising dataset among these DEMs and it could, therefore, be utilized for the studies and applications requiring accurate DEMs.