3D surface matching by local feature descriptors is a fundamental task in 3D object registration, recognition, and retrieval. In view of 2D projected descriptors' information compression and 3D directly voxelized descriptors' sensitivity to density variation and boundary, this paper first proposes a voxel-based buffer-weighted binary descriptor, named VBBD. After local surfaces of detected keypoints are voxelized, each voxel's buffer region is established, and the buffer-weighted Gaussian kernel density is calculated. If the current voxel's buffer-weighted density is larger than its local surface's average density, the voxel is labeled 1, otherwise, it is 0. The proposed descriptor has several merits: 1) direct acquisition of 3D information without projection, the neighbor information is less compressed. 2) voxels are labeled and binarized according to the buffer-weighted density, which improves the robustness to boundary effect, noise and density variation. Based on the VBBD, a global optimal surface matching method based on a Kuhn_Munkres (KM) algorithm is adopted. The strategy has several advantages: 1) by calculating the descriptors of large-scaled surfaces which are down sampled, the number of the point cloud is reduced, and meanwhile, large-scaled information is obtained; and 2) KM algorithm is adopted to find matching pairs to achieve final maximum weight sum of all matching pairs, which can efficiently avoid local optimum. The experimental results show that, compared with other state-of-the-art descriptors, the VBBD has better descriptiveness and robustness, and the surface matching strategy by the VBBD can achieve both high recall and precision.INDEX TERMS Voxel, Gaussian kernel density, binary descriptor, Kuhn_Munkres matching.