Accurate long-term streamflow and flood forecasting has always been an important research direction in hydrology research. Nowadays, with climate change, floods, and other anomalies occurring more and more frequently and bringing great losses to society. The prediction of streamflow, especially flood prediction, is important for disaster prevention. Current hydrological models based on physical mechanisms can give accurate predictions of streamflow, but the effective prediction period is only about one month in advance, which is too short for decision making. Previous studies have shown a link between the El Niño–Southern Oscillation (ENSO) and the streamflow of the Yangtze River. In this paper, we use ENSO and the monthly streamflow data of the Yangtze River from 1952 to 2016 to predict the monthly streamflow of the Yangtze River in two extreme flood years by using deep neural networks. In this paper, three deep neural network frameworks are used: Stacked LSTM, Conv LSTM Encoder-Decoder LSTM and Conv LSTM Encoder-Decoder GRU. Experiments have shown that the months of flood occurrence and peak flows predicted by these four models become more accurate after the introduction of ENSO. And the best results were obtained on the Convolutional LSTM + Encoder Decoder Gate Recurrent Unit model.