Time-series anomaly detection is an important research topic in data mining, popular in both academia and industry. Recently, unsupervised anomaly detection draws considerable attention, since it can detect anomalies without parameter tuning on labels and meets the demands of industrial applications. Time-series representation learning plays a vital role in addressing unsupervised anomaly detection. However, it remains challenging to learn a unified representation model with diverse distributions and handle multivariate times-series with various features.To alleviate these challenges, we propose a novel representation strategy, termed CAT-AD, for unsupervised time-series anomaly detection. It learns characteristic-aware priors for representations of time-series by incorporating embeddings of broad characteristics and is capable of handling diverse anomaly detection tasks, regardless of their lengths and dimensions.Our proposed strategy is simple yet effective, which has been verified on two univariate datasets and five multivariate datasets from public sources.