Satellite telemetry data contains satellite status information, and ground-monitoring personnel need to promptly detect satellite anomalies from these data. This paper takes the satellite power subsystem as an example and presents a reliable anomaly detection method. Due to the lack of abnormal data, the autoencoder is a powerful method for unsupervised anomaly detection. This study proposes a novel stage-training denoising autoencoder (ST-DAE) that trains the features, in stages. This novel method has better reconstruction capabilities in comparison to common autoencoders, sparse autoencoders, and denoising autoencoders. Meanwhile, a cluster-based anomaly threshold determination method is proposed. In this study, specific methods were designed to evaluate the autoencoder performance in three perspectives. Experiments were carried out on real satellite telemetry data, and the results showed that the proposed ST-DAE generally outperformed the autoencoders, in comparison.