Online fake news can generate a negative impact on both users and society. Due to the concerns with spread of fake news and misinformation, assessing the network influence of online users has become an important issue. This study quantifies the influence of nodes by proposing an algorithm based on information entropy theory. Dynamic process of influence of nodes is characterized on mobile social networks (MSNs). Weibo (i.e., the Chinese version of microblogging) users are chosen to build the real network and quantified influence of them is analyzed according to the model proposed in this paper. MATLAB is employed to simulate and validate the model. Results show the comprehensive influence of nodes increases with the rise of two factors: the number of nodes connected to them and the frequency of their interaction. Indirect influence of nodes becomes stronger than direct influence when the network scope rises. This study can help relevant organizations effectively oversee the spread of online fake news on MSNs.