Abstract: To facilitate the dispatch of energy systems, joint forecasting of electric, thermal, and cooling loads of integrated energy systems is required. Aiming at the complex influencing factors of multi-load in integrated energy systems, firstly, the factors that have a greater impact on the multi-load load are screened out through grey correlation analysis. The load is then predicted using a traditional long short-term memory(LSTM) neural network. Secondly, the prediction error is trained by the gated recurrent unit(GRU) to obtain the error compensation value. Finally, through the reconstruction of the load forecast value and the error forecast value, a more accurate load forecast value is obtained. The feasibility of the error compensation model is verified by comparing the effect of error compensation on prediction accuracy through examples, and the superiority of the proposed prediction method is demonstrated by comparing it with other two prediction models, which can improve the accuracy of multivariate load prediction.