Because of the mechanism of TLS system, noise, outliers, various occlusions, varying cloud densities, etc. inevitably exist in the collection of TLS point clouds. To achieve automatic TLS point cloud registration, many methods, based on the hand-crafted features of keypoints, have been proposed. Despite significant progress, the current methods still face great challenges in accomplishing TLS point cloud registration. In this paper, we propose a multi-scale neural network to learn local shape descriptors for establishing correspondences between pairwise TLS point clouds. To train our model, data augmentation, developed on pairwise semi-synthetic 3D local patches, is to extend our network to be robust to rotation transformation. Then, based on varying local neighborhoods, multi-scale subnetworks are constructed and fused to learn robust local features. Experimental results demonstrate that our proposed method successfully registers two TLS point clouds and outperforms state-of-the-art methods. Besides, our learned descriptors are invariant to translation and tolerant to changes in rotation.