El Niño-Southern Oscillation (ENSO) is an anomaly in the Tropical Pacific Ocean sea surface that can lead to extreme weather such as hail, floods, and typhoons, therefore, accurate prediction of ENSO is of great significance. An integrated graph convolutional network-transformer (GCNTR) model is presented in this paper. Firstly, transformer network is used to encode data features based on its strong focus ability of the global feature. Secondly, GCN is employed to extract features from graph data, and finally introduces a gated feature fusion mechanism to fuse the encoded features with the features extracted by GCN to achieve the accurate prediction ENSO. The results indicate that the GCNTR model achieves the prediction of ENSO 20 months in advance, which is 3 months longer than ENSOTR and 5 months longer than Transformer, and most of the prediction accuracy of the model is better than other models. Compared to the existing methods, the GCNTR model enables better prediction of ENSO.