Accurate multi-energy load forecasting is helpful to the rational planning and optimal operation of integrated energy systems. For solving the problems that it is very difficult to determine input parameters and set appropriate model network parameters in the multi-energy load forecasting model, a collaborative forecasting method for multi-energy load of building including electricity load, cooling load and heating load was developed. Firstly, considering the influence of different input parameters on multiple loads, the grey relation analysis (GRA) was used to calculate the correlation between input parameters and loads, and the parameters with values of grey relation greater than 0.6 were selected as the model inputs. At the same time, the grey wolf optimizer (GWO) was used to optimize the key network parameters of the long short-term memory neural network (LSTM), and the multi-energy load forecasting model of GRA-GWO-LSTM was developed. Finally, taking Arizona State University as an example, compared with the single neural network model and the hybrid neural network(GWO-LSTM) model, the proposed prediction model has higher prediction accuracy in long-term forecasting of electricity, cooling, and heating loads. Compared with the LSTM model and GWO-LSTM model, the mean absolute percentage error (MAPE) of the proposed prediction model is reduced by 31.64% and 23.47%, respectively. Furthermore, the GRA-GWO-LSTM model also has good predictive performance for short-term load forecasting and can be used to guide the design and intelligent operation of integrated energy systems.