Abstract. ENSO is an extremely sophisticated air-sea coupling phenomenon, the development and decay of which are usually modulated by the energy interactions between multiple physical variables. In this paper, we design a multivariate air-sea coupler (ASC) based on graph using features of multiple physical variables. On the basis of the coupler, an ENSO deep learning forecast model (named ENSO-ASC) is proposed, whose structure is adapted to the characteristics of the ENSO dynamics, including the encoder/decoder for capturing/restoring the multi-scale spatial-temporal correlations, and two attention components for grasping the different air-sea coupling strength on different start calendar month and varied contributions of physical variables in ENSO amplitudes. In addition, two datasets at different resolutions are used to train the model. We firstly tune the model performance to optimal and compare it with the other state-of-the-art ENSO deep learning forecast models. Then, we evaluate the ENSO forecast skill from the contributions of different predictors, the effective lead time with the different start calendar months, and the forecast spatial uncertainties, further analyze the underlying ENSO mechanisms. Finally, we make ENSO predictions over the validation period from 2014 to 2020. Experiment results demonstrate that ENSO-ASC outperforms the other models. Sea surface temperature (SST) and zonal wind are two crucial predictors. The correlation skill of Niño3.4 index is over 0.78/0.65/0.5 within the lead time of 6/12/18 months. From two heat map analyses, we also discover the common challenges in ENSO predictability, such as the forecasting skills declining faster when making forecasts through June-July-August and the forecast errors more likely showing up in the western-central equatorial Pacific with a longer lead time. ENSO-ASC can simulate El Niño and La Niña events with different strengths. The forecasted SST and wind patterns reflect obvious Bjerknes positive feedback mechanism. These results indicate the effectiveness and superiority of our model with the multivariate air-sea coupler in predicting sophisticated ENSO and analyzing the underlying dynamic mechanisms.