Brain medical image registration is the foundation of numerous clinical applications in neurosurgery, such as preoperative planning and intraoperative navigation. However, precise registration remains challenging when dealing with large-scale deformations between images to be registered and significant anatomical differences across modalities. Existing methods often incorporate explicit structure information (e.g., anatomical structure segmentation masks) as prior knowledge to assist registration, but obtaining high-precision structure prior knowledge itself is difficult. In addition, most existing methods for large-scale registration use low-resolution advanced semantic relationships as initial driving information for registration, which may mislead the registration process that relies primarily on structure alignment. To address these issues, this paper proposes a novel brain image registration method based on spatial structure inter-correlation. Specifically, we first extract shallow multi-scale anatomical structure information because the core of registration is the alignment of corresponding structures. Compared to deep structures rich in semantic information, shallow structures rich in structure information are more conducive to guiding the registration process. Then, we construct structure space inter-correlation based on the extracted shallow multi-scale anatomical structure information (including structure attention calculation between two modalities). Different scales of structure information contain different levels of structure inter-correlation, and by performing multi-level low-resolution upsampling and fusion, we obtain the final registration result to improve registration accuracy. Finally, starting from dual registration, the deformation from moving images to fixed images should enable fixed images to deform to moving images in the dual direction, thereby improving the robustness of registration. Through comparison with many advanced methods on brain MRI datasets, our proposed method demonstrates superior accuracy in brain images registration.