Learning discriminative features for effectively separating abnormal events from normality is crucial for weakly supervised video anomaly detection (WS-VAD) tasks. Existing approaches, both video and segment-level label oriented, mainly focus on extracting representations for anomaly data while neglecting the implication of normal data. We observe that such a scheme is sub-optimal, i.e., for better distinguishing anomaly one needs to understand what is a normal state, and may yield a higher false alarm rate. To address this issue, we propose an Uncertainty Regulated Dual Memory Units (UR-DMU) model to learn both the representations of normal data and discriminative features of abnormal data. To be specific, inspired by the traditional global and local structure on graph convolutional networks, we introduce a Global and Local Multi-Head Self Attention (GL-MHSA) module for the Transformer network to obtain more expressive embeddings for capturing associations in videos. Then, we use two memory banks, one additional abnormal memory for tackling hard samples, to store and separate abnormal and normal prototypes and maximize the margins between the two representations. Finally, we propose an uncertainty learning scheme to learn the normal data latent space, that is robust to noise from camera switching, object changing, scene transforming, etc. Extensive experiments on XD-Violence and UCF-Crime datasets demonstrate that our method outperforms the state-of-the-art methods by a sizable margin.