High-resolution DEMs can provide accurate geographic information and can be widely used in hydrological analysis, path planning, and urban design. As the main complementary means of producing high-resolution DEMs, the DEM super-resolution (SR) method based on deep learning has reached a bottleneck. The reason for this phenomenon is that the DEM super-resolution method based on deep learning lacks a part of the global information it requires. Specifically, the multilevel aggregation process of deep learning has difficulty sufficiently capturing the low-level features with dependencies, which leads to a lack of global relationships with high-level information. To address this problem, we propose a global-information-constrained deep learning network for DEM SR (GISR). Specifically, our proposed GISR method consists of a global information supplement module and a local feature generation module. The former uses the Kriging method to supplement global information, considering the spatial autocorrelation rule. The latter includes a residual module and the PixelShuffle module, which is used to restore the detailed features of the terrain. Compared with the bicubic, Kriging, SRCNN, SRResNet, and TfaSR methods, the experimental results of our method show a better ability to retain terrain features, and the generation effect is more consistent with the ground truth DEM. Meanwhile, compared with the deep learning method, the RMSE of our results is improved by 20.5% to 68.8%.