Settlement prediction is of great importance for safety control of concrete-face rockfill dams (CFRDs) during the operation stage. However, the prediction accuracy achieved by the commonly used hydrostatic–seasonal–time (HST) methods, without the consideration of the previous conditions of influencing factors, is not competitive. Moreover, in most methods, settlement data at each monitoring point are modeled individually; the correlation relationships between settlements are neglected. In this paper, a method based on an optimized long short-term memory (LSTM) model is proposed to predict the settlement of CFRDs, modeling multiple monitoring data series with strong correlation relationships simultaneously. In the method, settlement data series are classified into several categories, firstly according to a global relevance measure. Then, the cuckoo search (CS) algorithm is applied to optimize the hyper-parameters in the neural network structure of LSTM. Ultimately, the LSTM model is utilized to predict the multiple settlement data series classified in the same category. Results indicate that the proposed method has a better prediction performance compared with the LSTM model, the back propagation neural network (BPNN) model, and the HST with single monitoring point.