Relative pose estimation is crucial for various computer vision applications, including Robotic and Autonomous Driving. Current methods primarily depend on selecting and matching feature points prone to incorrect matches, leading to poor performance. Consequently, relying solely on point-matching relationships for pose estimation is a huge challenge. To overcome these limitations, we propose a Geometric Correspondence Graph neural network that integrates point features with extra structured line segments. This integration of matched points and line segments further exploits the geometry constraints and enhances model performance across different environments. We employ the Dual-Graph module and Feature Weighted Fusion Module to aggregate geometric and visual features effectively, facilitating complex scene understanding. We demonstrate our approach through extensive experiments on the DeMoN and KITTI Odometry datasets. The results show that our method is competitive with state-of-the-art techniques.