The formation of public opinion on the network is a hot issue in the field of complex network research, and some classical dynamic models are used to solve this problem. The signed network is a particular form of the complex network, which can adequately describe the amicable and hostile relationships in complex real-world systems. However, the methods for studying the dynamic process of public opinion propagation on signed networks still require to be further discussed. In this paper, the authors pay attention to the influence of negative edges in order to design a two-state public opinion propagation mechanism suitable for signed networks. The authors first set the interaction rules between nodes and the transition rules of node states and then apply the model to synthetic and real-world signed networks. The simulation results show that there is a critical value of the negative edge ratio. When the negative edge ratio exceeds this critical value, the evolutionary result of public opinion will change from a consistent state to a split state. This conclusion is also consistent with the distribution result of opinions within communities in the signed network. Besides, the research on the network structural balance shows that the model makes the network evolve in a more balanced direction.