We have used a set of Ground Control Points (GCPs) derived from altimetry measurements from the Ice, Cloud and land Elevation Satellite (ICESat) to evaluate the quality of the 30 m posting ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) Global Digital Elevation Model (GDEM) V3 elevation products produced by NASA/METI for Greenland and Antarctica. These data represent the highest quality globally distributed altimetry measurements that can be used for geodetic ground control, selected by applying rigorous editing criteria, useful at high latitudes, where other topographic control is scarce. Even if large outliers still remain in all ASTER GDEM V3 data for both, Greenland and Antarctica, they are significantly reduced when editing ASTER by number of scenes (N≥5) included in the elevation processing. For 667,354 GCPs in Greenland, differences show a mean of 13.74 m, a median of -6.37 m, with an RMSE of 109.65 m. For Antarctica, 6,976,703 GCPs show a mean of 0.41 m, with a median of -4.66 m, and a 54.85 m RMSE, displaying smaller means, similar medians, and less scatter than GDEM V2. Mean and median differences between ASTER and ICESat are lower than 10 m, and RMSEs lower than 10 m for Greenland, and 20 m for Antarctica when only 9 to 31 scenes are included.