Most state-of-the-art 3D object detectors rely heavily on LiDAR sensors and there remains a large gap in terms of performance between image-based and LiDAR-based methods, caused by inappropriate representation for the prediction in 3D scenarios. Our method, called Deep Stereo Geometry Network (DSGN), reduces this gap significantly by detecting 3D objects on a differentiable volumetric representation--3D geometric volume, which effectively encodes 3D geometric structure for 3D regular space. With this representation, we learn depth information and semantic cues simultaneously. For the first time, we provide a simple and effective one-stage stereo-based 3D detection pipeline that jointly estimates the depth and detects 3D objects in an end-to-end learning manner. Our approach outperforms previous stereo-based 3D detectors (about 10 higher in terms of AP) and even achieves comparable performance with a few LiDAR-based methods on the KITTI 3D object detection leaderboard. Code will be made publicly available at https://github. com/chenyilun95/DSGN.