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Dengue fever (DF) is one of the most rapidly spreading diseases in the world, and accurate forecasts of dengue in a timely manner might help local government implement effective control measures. To obtain the accurate forecasting of DF cases, it is crucial to model the long-term dependency in time series data, which is difficult for a typical machine learning method. This study aimed to develop a timely accurate forecasting model of dengue based on long short-term memory (LSTM) recurrent neural networks while only considering monthly dengue cases and climate factors. The performance of LSTM models was compared with the other previously published models when predicting DF cases one month into the future. Our results showed that the LSTM model reduced the average the root mean squared error (RMSE) of the predictions by 12.99% to 24.91% and reduced the average RMSE of the predictions in the outbreak period by 15.09% to 26.82% as compared with other candidate models. The LSTM model achieved superior performance in predicting dengue cases as compared with other previously published forecasting models. Moreover, transfer learning (TL) can improve the generalization ability of the model in areas with fewer dengue incidences. The findings provide a more precise forecasting dengue model and could be used for other dengue-like infectious diseases.