Accurate prediction of multi-energy load is essential for the scheduling, safe operation, and stability of integrated energy systems. This paper proposes a novel two-stage multi-energy load prediction model with dual-attention spatiotemporal joint network for integrated energy system. In the first stage of multi-task prediction, the integrated self-attention long short-term memory (LSTM) network is built to forecast the multi-energy load initially, and an error correction model on basis of BP network is constructed to reduce the impact of error accumulation on the second stage prediction. In the second stage of single-task prediction, a parallel spatiotemporal joint network model is proposed to extract the static spatial feature and dynamic temporal feature between multienergy loads and between loads and meteorological factors, which fully captures the complex interactions and dependencies between the multi-energy loads. The prediction model integrates self-attention and graph attention mechanisms in both stages to improve the feature extraction capabilities. The simulation results demonstrate that, compared to bidirectional LSTM, LSTM-gated recurrent unit, time convolutional networks-LSTM and variational mode decomposition-convolutional neural network-LSTM models, the proposed multi-energy load prediction model reduces the average absolute percentage error by 66.25%, 16.83%, 53.58% and 5.29%, respectively.