Multienergy load forecasting (MELF) is the premise of regional integrated energy systems (RIES) production planning and energy dispatch. The key of MELF is the consideration of multienergy coupling and the improvement of prediction accuracy. Therefore, a MELF method considering the multienergy coupling of variation characteristic curves (MELF_MECVCC) for RIES is proposed. The novelty of MELF_MECVCC lies in the following three aspects. 1) For the trend stripping and volatility extraction of multienergy load time series, the extreme-point symmetric mode decomposition-sample entropy (ESMD-SE) method is introduced to decompose and reconstruct the variation characteristic curves of multienergy, including trend curve and fluctuation curve. 2) The multienergy coupling of the variation characteristic curves is considered to reflect the variation characteristics of the multienergy loads. 3) Different methods are applied according to different variation characteristics; i.e., the combined method based on multitask learning and long short-term memory network (MTL-LSTM) is applied to predict the trend curve with strong correlation and the least square support vector regression (LSSVR) method is applied to predict the fluctuation curve with strong volatility and high complexity. Based on the actual data set of the University of Texas in Austin, the MELF_MECVCC model is simulated and verified, which shows that the model reduces the mean absolute percentage error (MAPE) and the root mean square error (RMSE) and fits better with the original load and has higher prediction accuracy, compared with current advanced algorithms.