Density estimation is a widely used method for unsupervised anomaly detection. However, the presence of anomalies in training data may severely impact the density estimation process, thereby hampering the use of more sophisticated density estimation methods such as those based on deep neural networks. In this work, we propose RobustRealNVP, a robust deep density estimation framework for unsupervised anomaly detection. Our approach differs from existing flow-based models from two perspectives. First, RobustRealNVP discards data points with low estimated densities during optimization to prevent them from corrupting the density estimation process. Furthermore, it imposes Lipschitz regularization to ensure smoothness in the estimated density function. We demonstrate the robustness of our algorithm against anomalies in training data from both theoretical and empirical perspectives. The results show that our algorithm outperforms state-of-the-art unsupervised anomaly detection methods.