Existing deep learning-based point cloud registration methods primarily focus on feature extraction and feature matching. However, the exploration of local and global graph structures during the feature extraction stage remains insufficient, and the investigation of difference information during the matching process is also limited. To address these issues, this study proposes a point cloud registration method based on local-global dynamic graph learning and complementary fusion. Specifically, the dynamic offset-based local graph learning module characterizes the underlying graph structure in the feature space by constructing proxy points that contain both geometric and semantic information, leading to more discriminative local features. In addition, a dynamic attention-based global graph learning module is designed, which adaptively adjusts attention weights based on the relationships between points, effectively capturing long-range dependencies in the point cloud. To further enhance the correspondence between the two point clouds, the attention-driven complementary fusion module utilizes the cross-attention mechanism to extract similar and distinctive information, while applying the self-attention mechanism to refine the relationships between features. Experimental results demonstrate that the proposed method achieves optimal registration performance on public datasets while maintaining acceptable computational efficiency.