As an essential step in the restoration of Terracotta Warriors, the results of fragments classification will directly affect the performance of fragments matching and splicing. However, most of the existing methods are based on traditional technology and have low accuracy in classification. A practical and effective classification method for fragments is an urgent need. In this case, an attention-based multi-scale neural network named AMS-Net is proposed to extract significant geometric and semantic features. AMS-Net is a hierarchical structure consisting of a multi-scale set abstraction block (MS-BLOCK) and a fully connected (FC) layer. MS-BLOCK consists of a local-global layer (LGLayer) and an improved multi-layer perceptron (IMLP). With a multi-scale strategy, LGLayer can parallel extract the local and global features from different scales. IMLP can concatenate the high-level and low-level features for classification tasks. Extensive experiments on the public data set (ModelNet40/10) and the real-world Terracotta Warrior fragments data set are conducted. The accuracy results with normal can achieve 93.52% and 96.22%, respectively. For real-world data sets, the accuracy is best among the existing methods. The robustness and effectiveness of the performance on the task of 3D point cloud classification are also investigated. It proves that the proposed end-to-end learning network is more effective and suitable for the classification of the Terracotta Warrior fragments.