Considering the situation that multi-agent systems subject to an external disturbance in the complex environment and malicious attacks in the controller, the leader-following quasi-consensus of a class of disturbed nonlinear multi-agent system under the impulsive control and an event-triggered mechanism is studied. Unlike existing literature that requires a minimum triggering interval to be specified in advance, Zeno behavior is avoided by setting appropriate parameters in the designed dynamic event-triggered mechanism. Based on this mechanism, some sufficient conditions to achieve quasi-consensus are further proposed, and the upper bound of error states is also estimated. Finally, a numerical simulation example verifies the feasibility of the results.