Video anomaly detection (VAD) has long been studied as a crucial problem in public security and crime prevention. In recent years, weakly-supervised VAD (WVAD) have attracted considerable attention due to their easy annotation process and promising research results. While existing WVAD methods tackle mainly on static datasets, the possibility that the domain of data can vary has been neglected. To adapt such domain-shift, the continual learning (CL) perspective is required because otherwise additional training only with new coming data could easily cause performance degradation for previous data, i.e., forgetting. Therefore, we propose a brand-new approach, called Continual Anomaly Detection with Ensembles (CADE) that is the first work combining CL and WVAD viewpoints. Specifically, CADE uses the Dual-Generator(DG) to address data imbalance and label uncertainty in WVAD. We also found that forgetting exacerbates the "incompleteness'' where the model becomes biased towards certain anomaly modes, leading to missed detections of various anomalies. To address this, we propose to ensemble Multi-Discriminator (MD) that capture missed anomalies in past scenes due to forgetting, using multiple models. Extensive experiments show that CADE significantly outperforms existing VAD methods on the common multi-scene VAD datasets, such as ShanghaiTech and Charlotte Anomaly datasets.