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. First, 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 directed topologies for containment control enables followers to track targets within a convex hull in finite time and stay within it as it changes. The sliding mode control makes the convergence more robust. Finally, simulation results demonstrate the effectiveness of the proposed method.