Centrifugal compressors are widely used in the petroleum and natural gas industry for gas compression, reinjection, and transportation. Early fault identification and fault evolution prediction for centrifugal compressors can improve equipment safety and reduce maintenance and operating costs. This article proposes a dynamic process monitoring method for centrifugal compressors based on long short-term memory (LSTM) and principal component analysis (PCA). This method constructs a sliding window for monitoring at each sampling point, which contains 100 data from the past and current time points, and uses LSTM to predict 30 future data points. At the same time, this method is also combined with the PCA threshold process monitoring method to construct a new LSTM-PCA monitoring algorithm. And the method was validated using centrifugal compressor process data. The results show that this method can effectively detect process anomalies, The improvements significantly reduced the false positive rate of detected anomalies, and can make multi-step advance predictions of system behavior after faults occur.