Anomaly detection is of great significance in condition-based maintenance of power plant equipment. The conventional fixed threshold detection method is not able to perform early detection of equipment abnormalities. In this study, a general anomaly detection framework based on a long short-term memory-based autoencoder (LSTM-AE) network is proposed. A normal behavior model (NBM) is established to learn the normal behavior patterns of the operating variables of the equipment in space and time. Based on the similarity analysis between the NBM output distribution and the corresponding measurement distribution, the Mahalanobis distance (MD) is used to describe the overall residual (OR) of the model. The reasonable range is obtained using kernel density estimation (KDE) with a 99% confidence interval, and the OR is monitored to detect abnormalities in real-time. An induced draft fan is chosen as a case study. Results show that the established NBM has excellent accuracy and generalizability, with average root mean square errors of 0.026 and 0.035 for the training and test data, respectively, and average mean absolute percentage errors of 0.027%. Moreover, the abnormal operation case shows that the proposed framework can be effectively used for the early detection of abnormalities.