Camera and 3D LiDAR sensors have become indispensable devices in modern autonomous driving vehicles, where the camera provides the fine-grained texture, color information in 2D space and LiDAR captures more precise and farther-away distance measurements of the surrounding environments. The complementary information from these two sensors makes the two-modality fusion be a desired option. However, two major issues of the fusion between camera and LiDAR hinder its performance, i.e., how to effectively fuse these two modalities and how to precisely align them (suffering from the weak spatiotemporal synchronization problem). In this paper, we propose a coarse-to-fine LiDAR and camera fusion-based network (termed as LIF-Seg) for LiDAR segmentation. For the first issue, unlike these previous works fusing the point cloud and image information in a one-to-one manner, the proposed method fully utilizes the contextual information of images and introduces a simple but effective early-fusion strategy. Second, due to the weak spatiotemporal synchronization problem, an offset rectification approach is designed to align these two-modality features. The cooperation of these two components leads to the success of the effective camera-LiDAR fusion. Experimental results on the nuScenes dataset show the superiority of the proposed LIF-Seg over existing methods with a large margin. Ablation studies and analyses demonstrate that our proposed LIF-Seg can effectively tackle the weak spatiotemporal synchronization problem.