Most existing methods for unsupervised industrial anomaly detection train a separate model for each object category. This kind of approach can easily capture the category-specific feature distributions, but results in high storage cost and low training efficiency. In this paper, we propose a unified mixed-attention auto encoder (MAAE) to implement multi-class anomaly detection with a single model. To alleviate the performance degradation due to the diverse distribution patterns of different categories, we employ spatial attentions and channel attentions to effectively capture the global category information and model the feature distributions of multiple classes. Furthermore, to simulate the realistic noises on features and preserve the surface semantics of objects from different categories which are essential for detecting the subtle anomalies, we propose an adaptive noise generator and a multi-scale fusion module for the pre-trained features. MAAE delivers remarkable performances on the benchmark dataset compared with the state-of-the-art methods.