A finite-time containment control based on a hybrid event-triggered mechanism is proposed to address the issue of limited communication resources in multi-agent systems (MASs), where the event-triggered mechanism is extended from the followers to the leaders. To begin with, dedicated event-triggered functions are designed for both followers and leaders, enabling event-triggered communication for both followers and leaders, with controller updates for followers. Furthermore, state-dependent adaptive parameters are designed in the triggering functions to dynamically adjust the triggering thresholds, thereby reducing the frequency of event-triggered actions. Applying the proposed method to MASs under directed topology can achieve containment control within a finite time. Finally, simulation results demonstrate the effectiveness of the new method.