In order to improve the accuracy of the multiple load forecasting of a regional integrated energy system, a short-term multiple load forecasting model based on the quantum weighted GRU and multi-task learning framework is proposed in this paper. Firstly, correlation analysis is carried out using a maximum information coefficient to select the input of the model. Then, a multi-task learning architecture is constructed based on the quantum weighted GRU neural network, and the coupling information among multiple loads is learned through the sharing layer in order to improve the prediction accuracy of multiple loads. Finally, the PSO algorithm is used to optimize the parameters of the quantum weighted GRU. The simulation data of a regional integrated energy system in northern China are used to predict the power and cooling loads on summer weekdays and rest days, and the results show that, compared with the LSTM, GRU and single task learning QWGRU models, the proposed model is more effective in the multiple load forecasting of a regional integrated energy system.