Three-dimensional point cloud anomaly detection that aims to detect anomaly data points from a training set serves as the foundation for a variety of applications, including industrial inspection and autonomous driving. However, existing point cloud anomaly detection methods often incorporate multiple feature memory banks to fully preserve local and global representations, which comes at the high cost of computational complexity and mismatches between features. To address that, we propose an unsupervised point cloud anomaly detection framework based on joint local-global features, termed PointCore. To be specific, PointCore only requires a single memory bank to store local (coordinate) and global (PointMAE) representations and different priorities are assigned to these local-global features, thereby reducing the computational cost and mismatching disturbance in inference. Furthermore, to robust against the outliers, a normalization ranking method is introduced to not only adjust values of different scales to a notionally common scale, but also transform densely-distributed data into a uniform distribution. Extensive experiments on Real3D-AD dataset demonstrate that PointCore achieves competitive inference time and the best performance in both detection and localization as compared to the state-of-the-art Reg3D-AD approach and several competitors.