Anomaly detection plays an important role in prognostics health management (PHM) of satellites. In this article, a novel anomaly detection scheme based on long short-term memory (LSTM) networks is proposed to overcome the difficulties of nonlinear modeling in satellite power system. Firstly, the data-driven linear feedback model was reviewed, and parameter identification was provided. Subsequently, in order to enhance the modeling ability of nonlinear systems, LSTM networks were introduced. The combined effect of gate control design and nonlinear activation function enables it to model nonlinear systems well, thereby achieving more accurate prediction of dynamic time series data. Finally, the method proposed in this article is applied in anomaly detection experiments of satellite solar array driver group (SADA) systems. The results indicate that this method can effectively establish local models of nonlinear systems and predict system states over a period of time. Moreover, the expected low false positive rate and high detection rate were achieved, which were 9.18% and 98.37%, respectively.