Precisely predicting natural gas prices (NGPs) is important because it can provide the necessary decision-making basis for energy scheduling, planning and control. However, NGPs are affected by many factors and exhibit the characteristics of nonlinearity and randomness, which makes accurate predictions challenging. Therefore, in this paper, the information gain of multisource data and the global optimization ability of the gray wolf algorithm are used to build a multifactor-driven NGP hybrid forecasting model to improve the prediction performance. First, the emotional tendency and readability of news text are extracted and calculated by using VADER and textstat tools, respectively. Then the network search index is filtered and integrated by using the correlation coefficient method and the CRITIC method to form alternative variables of multisource data (news and search index). Second, the gray wolf optimization algorithm is used to find and determine the best key parameter group in long short-term memory model. Finally, the spot price of natural gas in Henry Hub from March 1, 2012 to February 28, 2022 is selected as the prediction object, and multi-scenario numerical experiments are carried out to verify the effectiveness of the proposed model. The ablation experiment results show that the information gain brought by multisource data can effectively improve the prediction effect of NGPs. Furthermore, the proposed model has the best prediction performance in different scenarios and can be regarded as a promising prediction tool.