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High-quality surface normal can help improve geometry estimation in problems faced by autonomous vehicles, such as collision avoidance and occlusion inference. While a considerable volume of literature focuses on densely scanned indoor scenarios, normal estimation during autonomous driving remains an intricate problem due to the sparse, non-uniform, and noisy nature of real-world LiDAR scans. In this paper, we introduce a multi-modal technique that leverages 3D point clouds and 2D colour images obtained from LiDAR and camera sensors for surface normal estimation. We present the Hybrid Geometric Transformer (HGT), a novel transformer-based neural network architecture that proficiently fuses visual semantic and 3D geometric information. Furthermore, we developed an effective learning strategy for the multi-modal data. Experimental results demonstrate the superior effectiveness of our information fusion approach compared to existing methods. It has also been verified that the proposed model can learn from a simulated 3D environment that mimics a traffic scene. The learned geometric knowledge is transferable and can be applied to real-world 3D scenes in the KITTI dataset. Further tasks built upon the estimated normal vectors in the KITTI dataset show that the proposed estimator has an advantage over existing methods.