This article focuses on the security control for general linear multi-agent systems (MASs) against false data injection attacks (FDIAs). A dynamic edge-based event-triggered mechanism is proposed, which reduces bandwidth consumption, saves communication resources and avoids continuous communication between agents. First, a neighbor information estimator is designed for each agent to match the asynchronous information generated by the dynamic edge-based event-triggered mechanism. A state estimator is designed to monitor and quantify the impact of FDIAs, while a feedback compensation mechanism is implemented in the control loop to mitigate attack-induced disturbances. Further, it is proved that the consensus control can be realized without Zeno behavior. Finally, a numerical simulation example is used to prove the effectiveness of the proposed method.