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As an important index of solar activity, the 10.7-cm solar radio flux (F10.7) can indicate changes in the solar EUV radiation, which plays an important role in the relationship between the Sun and the Earth. Therefore, it is valuable to study and forecast F10.7. In this study, the long short-term memory (LSTM) method in machine learning is used to predict the daily value of F10.7. The F10.7 series from 1947 to 2019 are used. Among them, the data during 1947–1995 are adopted as the training dataset, and the data during 1996–2019 (solar cycles 23 and 24) are adopted as the test dataset. The fourfold cross validation method is used to group the training set for multiple validations. We find that the root mean square error (RMSE) of the prediction results is only 6.20~6.35 sfu, and the correlation coefficient (R) is as high as 0.9883~0.9889. The overall prediction accuracy of the LSTM method is equivalent to those of the widely used autoregressive (AR) and backpropagation neural network (BP) models. Especially for 2-day and 3-day forecasts, the LSTM model is slightly better. All this demonstrates the potentiality of the LSTM method in the real-time forecasting of F10.7 in future.