The negative public opinions and views on overseas direct investment (ODI) of a multinational enterprise (MNE) will damage the image of its brand and are likely to bring it serious economic and social losses. So, it is important for the MNE to understand the formation and spread mechanism of public opinion risk (POR) in order to effectively respond to and guide the public opinion. This research proposed a multifractal-based situation optimization method to explore the POR evolution based on the media-based negative sentiment on China’s ODI. The sentiment measurement is obtained by a directed crawler for gathering the text of media reports corresponding to a certain ODI event using a URL knowledge base from the GDELT Event Database. Taking the public opinion crisis of the tax evasion incident of the local arm of China’s MNE in India as an example, the experiments show that this method could dynamically monitor the POR event in real-time and help MNE guide the effective control and benign evolution of public opinion of the event.