This paper studies the differentially private consensus problem of multiagent networks by employing a distributed event-triggered mechanism such that not only agents can protect the privacy of their initial states from information disclosure, but the execution efficiency of the whole network can be improved. First, we propose a distributed event-triggered mechanism for a differentially private consensus algorithm such that frequent real-time communication and controller updates can be avoided. Second, we propose a distributed event-triggering condition that only depends on local information and local parameters, which can effectively avoid global information collection. Third, the convergence analysis of the mean-square average consensus is given to explain the sufficiency of the proposed event-triggered mechanism and event-triggering condition. Furthermore, we establish the statistic properties of the convergent accuracy that the expectation of the convergence point converges to the average value of all agents' initial states exactly and the disturbance variance is bounded with an explicit expression. In addition, we further give the differential privacy analysis that each agent can flexibly select its own privacy level to prevent information disclosure. Finally, simulation results are given to illustrate the effectiveness of the proposed mechanism and the correctness of the theoretical results.