To meet the challenges of energy sustainability, the integrated energy system (IES) has become a key component in promoting the development of innovative energy systems. Accurate and reliable multivariate load prediction is a prerequisite for IES optimal scheduling and steady running, but the uncertainty of load fluctuation and many influencing factors increase the difficulty of forecasting. Therefore, this article puts forward a multi-energy load prediction approach of the IES, which combines the fennec fox optimization algorithm (FFA) and hybrid kernel extreme learning machine. Firstly, the comprehensive weight method is used to combine the entropy weight method and Pearson correlation coefficient, fully considering the information content and correlation, selecting the key factors affecting the prediction, and ensuring that the input features can effectively modify the prediction results. Secondly, the coupling relationship between the multi-energy load is learned and predicted using the hybrid kernel extreme learning machine. At the same time, the FFA is used for parameter optimization, which reduces the randomness of parameter setting. Finally, the approach is utilized for the measured data at Arizona State University to verify its effectiveness in multi-energy load forecasting. The results indicate that the mean absolute error (MAE) of the proposed method is 0.0959, 0.3103 and 0.0443, respectively. The root mean square error (RMSE) is 0.1378, 0.3848 and 0.0578, respectively. The weighted mean absolute percentage error (WMAPE) is only 1.915%. Compared to other models, this model has a higher accuracy, with the maximum reductions on MAE, RMSE and WMAPE of 0.3833, 0.491 and 2.8138%, respectively.