Ground elevation estimation is vital for numerous applications in autonomous vehicles and intelligent robotics including three-dimensional object detection, navigable space detection, point cloud matching for localization, and registration for mapping. However, most works regard the ground as a plane without height information, which causes inaccurate manipulation in these applications. In this work, we propose GeeNet, a novel end-to-end, lightweight method that completes the ground in nearly real time and simultaneously estimates the ground elevation in a grid-based representation. GeeNet leverages the mixing of two- and three-dimensional convolutions to preserve a lightweight architecture to regress ground elevation information for each cell of the grid. For the first time, GeeNet has fulfilled ground elevation estimation from semantic scene completion. We use the SemanticKITTI and SemanticPOSS datasets to validate the proposed GeeNet, demonstrating the qualitative and quantitative performances of GeeNet on ground elevation estimation and semantic scene completion of the point cloud. Moreover, the crossdataset generalization capability of GeeNet is experimentally proven. GeeNet achieves state-of-the-art performance in terms of point cloud completion and ground elevation estimation, with a runtime of 0.88 ms.