Based on the consistency principle, an event-triggered asynchronous communication protocol is proposed to solve the parameter identification problem of distributed multi-agent systems represented by Box- Jenkins multi-models. Firstly, the event triggering mechanism is designed by using the parameter estimation information of agents, and the activation function is introduced to determine the communication triggering between agents. Secondly, the auxiliary model is used to solve the issue of the unobservable noise and internal variables. Then, the theory of multi-innovation is introduced into the communication protocol to improve the accuracy of parameter estimation. In the case of undirected connectivity of network topology, each agent updates the model parameters iteratively in a fully distributed way On the basis, the convergence of the algorithm is discussed. Finally, the effectiveness of the proposed method is verified by the results of the simulation example.