With the development of China's Belt and Road Initiative (BRI), the port plays a significant role and its operation management faces some pressure. In this regard, prediction of daily container volumes will provide the manager with data support for better plan of a storage yard. In this work, by deep learning the historical dataset, the long short-term memory (LSTM) recurrent neural network (RNN) is trained and used to predict daily volumes of containers which will enter the storage yard. The raw dataset of a certain port from 2013 to 2016 is chosen as the training set and the dataset of 2017 is used as the test set to evaluate the performance of the proposed prediction model. Then the LSTM model is established with Python and Tensorflow framework. The structure parameters are adjusted to find the optimal LSTM network, so as to improve the prediction accuracy. It appears that the LSTM model with two hidden layers and 30 hidden layer units has less prediction error between the real data and predicted data of 2017. The prediction error of daily container volumes between predicted value and real data of 2017 is about 12.39%, which is less than the people-predicted error. It is promising that the proposed LSTM RNN model can be applied to predict the daily volumes of containers and have higher prediction accuracy.