This paper studies the problem of event-based secure consensus for multi-agent systems subject to asynchronous denial of service attacks. The case that the communication network of multi-agent systems only contains a directed spanning tree is considered. Subsequently, we conduct a precise analysis of frequency and duration of denial of service attacks. Then, we regard the multi-agent system suffering from the invalid denial of service attack as a multi-agent system with switching topology, and adopt the control method of dealing with the switching topology to reduce the impact of invalid denial of service attacks on the multi-agent system. In addition, we propose a event-triggered resilient control mechanism, which enables multi-agent systems to reach consensus at an exponentially convergent speed, and prevents multi-agent systems from Zeno behavior, thereby avoiding continuous communication between agents. A simulation example is given to verify the correctness of the theoretical analysis.