Information inside visual and LiDAR data is well complementary derived from the fine-grained texture of images and massive geometric information in point clouds. However, it remains challenging to explore effective visual-LiDAR fusion, mainly due to the intrinsic data structure inconsistency between two modalities: Image pixels are regular and dense, but LiDAR points are unordered and sparse. To address the problem, we propose a local-to-global fusion network (DVLO) with bi-directional structure alignment. To obtain locally fused features, we project points onto the image plane as cluster centers and cluster image pixels around each center. Image pixels are pre-organized as pseudo points for image-to-point structure alignment. Then, we convert points to pseudo images by cylindrical projection (point-to-image structure alignment) and perform adaptive global feature fusion between point features and local fused features. Our method achieves state-of-the-art performance on KITTI odometry and FlyingThings3D scene flow datasets compared to both single-modal and multi-modal methods. Codes are released at https://github.com/IRMVLab/DVLO .