This paper aims to develop a nonrigid registration method of preoperative and intraoperative thoracoabdominal CT images in computer-assisted interventional surgeries for accurate tumor localization and tissue visualization enhancement. However, fine structure registration of complex thoracoabdominal organs and large deformation registration caused by respiratory motion is challenging. To deal with this problem, we propose a 3D multi-scale attention VoxelMorph (MA-VoxelMorph) registration network. To alleviate the large deformation problem, a multi-scale axial attention mechanism is utilized by using a residual dilated pyramid pooling for multi-scale feature extraction, and position-aware axial attention for long-distance dependencies between pixels capture. To further improve the large deformation and fine structure registration results, a multi-scale context channel attention mechanism is employed utilizing content information via adjacent encoding layers. Our method was evaluated on four public lung datasets (DIR-Lab dataset, Creatis dataset, Learn2Reg dataset, OASIS dataset) and a local dataset. Results proved that the proposed method achieved better registration performance than current state-of-the-art methods, especially in handling the registration of large deformations and fine structures. It also proved to be fast in 3D image registration, using about 1.5 s, and faster than most methods. Qualitative and quantitative assessments proved that the proposed MA-VoxelMorph has the potential to realize precise and fast tumor localization in clinical interventional surgeries.