Digital Elevation Models (DEMs) of Greenland provide the basic data for studying the Greenland ice sheet (GrIS), but little research quantitatively evaluates and compares the accuracy of various Greenland DEMs. This study uses IceBridge elevation data to evaluate the accuracies of the the Greenland Ice Map Project (GIMP)1 DEM, GIMP2 DEM, TanDEM-X, and ArcticDEM in their corresponding time ranges. This study also analyzes the impact of DEM accuracy and resolution on the accuracy of river network extraction. The results show that (1) within the time range covered by each DEM, TanDEM-X with an RMSE of 5.60 m has higher accuracy than the other DEMs in terms of absolute height accuracy, while GIMP1 has the lowest accuracy among the four Greenland DEMs, with an RMSE of 14.34 m. (2) Greenland DEMs are affected by regional errors and interannual changes. The accuracy in areas with elevations above 2000 m is higher than that in areas with elevations below 2000 m, and better accuracy is observed in the north than in the south. The stability of the ArcticDEM product is higher than those of the other three DEM products, and its RMSE standard deviation over multiple years is only 0.14 m. Therefore, the errors caused by the applications of DEMs with longer time spans are smaller. GIMP1 performs in an opposite manner, with a standard deviation of 2.39 m. (3) The river network extracted from TanDEM-X is close to the real river network digitized from remote sensing images, with an accuracy of 50.78%. The river network extracted from GIMP1 exhibits the largest errors, with an accuracy of only 8.83%. This study calculates and compares the accuracy of four Greenland DEMs and indicates that TanDEM-X has the highest accuracy, adding quantitative studies on the accuracy evaluation of various Greenland DEMs. This study also compares the results of different DEM river network extractions, verifies the impact of DEM accuracy on the accuracy of the river network extraction results, and provides an explorable direction for the hydrological analysis of Greenland as a whole.