3D Anomaly Detection (AD) is a promising means of controlling the quality of manufactured products. However, existing methods typically require carefully training a task-specific model for each category independently, leading to high cost, low efficiency, and weak generalization. Therefore, this paper presents a novel unified model for Multi-Category 3D Anomaly Detection (MC3D-AD) that aims to utilize both local and global geometry-aware information to reconstruct normal representations of all categories. First, to learn robust and generalized features of different categories, we propose an adaptive geometry-aware masked attention module that extracts geometry variation information to guide mask attention. Then, we introduce a local geometry-aware encoder reinforced by the improved mask attention to encode group-level feature tokens. Finally, we design a global query decoder that utilizes point cloud position embeddings to improve the decoding process and reconstruction ability. This leads to local and global geometry-aware reconstructed feature tokens for the AD task. MC3D-AD is evaluated on two publicly available Real3D-AD and Anomaly-ShapeNet datasets, and exhibits significant superiority over current state-of-the-art single-category methods, achieving 3.1\% and 9.3\% improvement in object-level AUROC over Real3D-AD and Anomaly-ShapeNet, respectively. The source code will be released upon acceptance.