Monocular 6D pose estimation is a fundamental task in computer vision. Existing works often adopt a two-stage pipeline by establishing correspondences and utilizing a RANSAC algorithm to calculate 6 degrees-of-freedom (6DoF) pose. Recent works try to integrate differentiable RANSAC algorithms to achieve an end-to-end 6D pose estimation. However, most of them hardly consider the geometric features in 3D space, and ignore the topology cues when performing differentiable RANSAC algorithms. To this end, we proposed a Depth-Guided Edge Convolutional Network (DGECN) for 6D pose estimation task. We have made efforts from the following three aspects: 1) We take advantages ofestimated depth information to guide both the correspondences-extraction process and the cascaded differentiable RANSAC algorithm with geometric information. 2)We leverage the uncertainty ofthe estimated depth map to improve accuracy and robustness ofthe output 6D pose. 3) We propose a differentiable Perspective-n-Point(PnP) algorithm via edge convolution to explore the topology relations between 2D-3D correspondences. Experiments demonstrate that our proposed network outperforms current works on both effectiveness and efficiency.