As industrial production environments become more and more complex, demand for three-dimensional point cloud industrial anomaly detection is increasing. Although the two-dimensional anomaly detection methods based on pre-trained network have significant effects, generalization ability of the three-dimensional point cloud pre-training network is limited, which leads to poor effect of this kind of point cloud anomaly detection methods. To improve performance of the three-dimensional point cloud anomaly detection, Point-ReAD, an anomaly detection method based on point cloud reconstruction, was proposed. The proposed method consists of an anomaly simulation module, a point cloud reconstruction network, and an anomaly discrimination module. In specific, during training phase, anomalous point clouds were created from normal point cloud maps by the anomaly simulation module, with the normal point clouds served as self-supervised signals to guide the learning process of the reconstruction network; in the point cloud reconstruction network, Group Attention Module (GAM) was used to design complex structural information for point cloud integration, thereby capturing geometric and semantic features in point clouds effectively; in the inference phase, the tested point clouds were input to the reconstruction network to generate reconstructed point clouds, and anomalies were located accurately through the anomaly discrimination module by comparing the point clouds before and after reconstruction. Experimental results show that Point-ReAD achieves the PC-AUROC (PointCloud level Area Under the Receiver Operator characteristic Curve) and the point-level AUPRO (Area Under the Per-Region Overlap) of 95.49% and 94.66%, respectively, on MVTec 3D-AD dataset, which are improved by 0.89, 1.27 percentage points, compared to subprior method 3DR?M (3D Discriminatively trained Reconstruction Anomaly Embedding Model).