A generalized opinion dynamics model (GODM) was proposed. This model dynamically computed each person’s expressed opinion to solve the opinion maximization problem for social trust networks. In the model, a new, reasonable and interpretable confidence index α_i was proposed. This index was determined by both person’s social status and the evaluation of his/her predecessors. By using the theory of diagonally dominant, the optimal analytic solution of the Nash equilibrium with maximum overall opinion was obtained. In addition, an efficient traditional ADMM algorithm with l₁-regulations to maximize the overall opinion was designed. A series of experiments were conducted, and the experimental results show that the proposed method is superior to the state-of-the-art in four datasets. The average benefit has been improved by 66.4%, 88.7%, 47.8% and 34.1% in solving the internal opinion problem. The experimental results fully verify the superiority of the proposed model.