The increasing dependence of power system and natural gas system in energy Internet brings higher challenge to the load forecasting of power system and natural gas system in integrated energy system. In this paper, a combined load forecasting method for electricity and gas based on long-short term memory network and weight sharing is proposed. In the prediction model, firstly, the correlation coefficient is used to analyze the weather factors, and the important weather factors of the two loads are extracted. The long-short term memory network is used as the main forecasting algorithm, and the weight sharing mode is used to analyze the correlation between the electricity and gas loads. An example is given to verify the effectiveness of the algorithm by using the data of Yunnan integrated energy system demonstration project. The results show that the algorithm proposed in this paper can effectively improve the accuracy of electricity-natural gas load forecasting in the integrated energy system, which has high application value.