Owing to its significance and high demand, various practical applications call for an effective anomaly detection method. However, most time series anomaly detection models lack robustness, tending to suffer from noise and outliers in the training sets, and thus always achieve suboptimal anomaly detection performance in the real world. To tackle this problem, in this thesis, we propose Gated Recurrent Unit - Robust Variational Autoencoder (GRU-RVAE), an unsupervised anomaly detection model for multivariate time series data. GRU-RVAE applies bidirectional Gated Recurrent Units to model informative dependences among time series, and Variational Autoencoder with a modified loss function to process noise and outliers in the training stage explicitly, learn the data distribution of normal time series, and detect anomalies. We conduct experiments on two representative multivariate time series datasets, and experimental results show GRU-RVAE outperforms four state-of-art baselines in both anomaly detection performance and robustness, achieving improvements of 2.7 ∼ 6.6 % in the best F1-scores for different levels of noise and outliers in the training sets.