Using a multi-agent system to control network is an important method to manipulate controllable networks. The reasonable control of network is based on the belief reachability of the multi-agent system, which means that the belief of every agent must be consistent with the real state of the network before making decisions. To research the belief reachability and convergence rate of the multi-agent system, a new model named multi-agent system belief distance updating model, which describes the updating progress of distance between agent’s belief and real network state, is proposed based on the traditional belief updating model. And the rationality of the new model is also proved. The model which transforms the belief updating progress into a linear system simplifies the analysis of belief reachability and convergence rate of the multi-agent system. Based on this model, a sufficient and necessary condition for belief reachability, and the upper limit of convergence rate of multi-agent system are proved. Besides, the belief reachability and the convergence rate of the multi-agent system in complete coupling network and scale-free network are also discussed respectively considering the characteristics of the two complicated networks. The model is adaptable to all multi-agent environments, and provides a good tool to analyze the belief reachability of the multi-agent system.