To construct a three-dimensional (3D) model of a tooth, multiple charge coupled device (CCD) cameras should be deployed in practice. Each CCD camera captures part of the tooth from a different angle. The images captured by different cameras must be registered to construct the relational 3D model. Sample consensus initial alignment (SAC-IA) algorithm is usually adopted, and fast point feature histograms (FPFH) descriptor is selected to calculate eigenvalues for different images. However, the original SAC-IA algorithm cannot satisfy a real-time application because of low efficiency and accuracy. According to the application of voxel nearest neighbor search in octree in 3D data search, this paper proposes an improved SAC-IA algorithm based on voxel nearest neighbor search to improve the efficiency and accuracy of the algorithm. The experimental results show that comparing to the traditional SAC-IA algorithm, the proposed algorithm based on voxel nearest neighbor search improves the efficiency by 20.95% and the registration accuracy by 24.95%. The improved algorithm can be deployed to construct a 3D model of a tooth as well as 3D model construction of other objects based on coded structured light.