In this paper,we propose a long short-term memory (LSTM) deep learning model to deal with the smoothed monthly sunspot number (SSN),aiming to address the problem whereby the prediction results of the existing sunspot prediction methods are not uniform and have large deviations.Our method optimizes the number of hidden nodes and batch sizes of the LSTM network structures to 19 and 20,respectively.The best length of time series and the value of the timesteps were then determined for the network training,and one-step and multi-step predictions for Cycle 22 to Cycle 24 were made using the well-established network.The results showed that the maximum root-mean-square error (RMSE) of the one-step prediction model was 6.12 and the minimum was only 2.45.The maximum amplitude prediction error of the multi-step prediction was 17.2％ and the minimum was only 3.0％.Finally,the next solar cycles (Cycle 25) peak amplitude was predicted to occur around 2023,with a peak value of about 114.3.The accuracy of this prediction method is better than that of the other commonly used methods,and the method has high applicability.