Shuttle Radar Topography Mission(SRTM) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) GDEM have a high spatial resolution and wide spatial coverage, which play an important role in many Earth researches. However, their error distributions are heterogeneous on different terrain types. In order to assess the elevation accuracy of the two DEMs, data from Geoscience Laser Altimeter System (GLAS) carried on the Ice, Cloud, and land Elevation Satellite (ICESat) are often used as the checkpoints due to their high accuracy. Taking Shandong Province as the research area, the accuracy of SRTM and ASTER GDEM are first evaluated by ICESat/GLAS in the years of 2003-2010 in this paper. Results indicate that the root mean squared errors (RMSEs) of SRTM and ASTER are 5.57 m and 7.20 m, respectively, which are much lower than the nominated accuracy. We further analyzed the effect of terrain slope and landscape type on the accuracy of SRTM and ASTER GDEM. Specifically, the study area was first divided into different sub-regions according to slope ranges (0~5°, 5~10°, 10~15°, 15~20°, 20~25°, 30~35°, 35~40°, 40~45°) and landscape types (farmland, shrub, forest, grassland, wetlands, water body), respectively. Then, the RMSE of each sub-region was computed and analyzed. We found that with the increasing of terrain slope, the accuracy of the two DEMs decreases, and under different land cover types, they also have different accuracy. More specifically, the two DEMs have a higher accuracy on farmland and shrub; while have a lower accuracy on forest and wet lands. To improve the accuracy of SRTM and ASTER, their error surfaces were first produced by interpolating the elevation differences between the DEM and randomly selected ICESat/GLAS data with the proportion of 90%. The interpolation methods include Inverse Distance Weight (IDW), Ordinary Kriging (OK), terrain-to-grid method (T2G) and Natural Neighborhood (NN). Then, the interpolated error surfaces were added to the original DEMs. Accuracy assessment of the improved SRTM and ASTER using the remaining 10% ICESat/GLAS demonstrates that IDW with the RMSEs of 2.20 m and 5.31 m is more accurate than the other interpolation methods. IDW is closely followed by T2G and NN. It is surprised to see that OK produces the worst results. Hence, SRTM and ASTER GDEM are improved with the IDW-based error surfaces. The ICESat-2 satellite was launched on September 15, 2018. It can emit 10,000 laser pulses per second, monitoring the height of glaciers and land in unprecedented detail. ICESat-2 collects elevation data over all surfaces spanning the world's frozen regions, forests, lakes, urban areas, and more. Thus, further researches will focus on improving the accuracy of SRTM and ASTER with the ICESat2 data.