For handling the broken-down communication infrastructure when a disaster event happens, this paper proposes to dispatch the unmanned aerial vehicle (UAV) to the disaster area as the relay node, which further forms a Flying Ad hoc Network (FANET). Since the UAV only owns limited energy and a disaster event may need multiple UAVs to cover its area, an efficient multi-UAV dispatch algorithm is critical to recover the communication link of the disaster area. In this paper, we adopt the mobile ground control station (GCS) to transport UAVs to the boundary of the disaster area first. According to the UAV energy consumption rate during flight and two communication modes, the UAV charging progress, and the number of required UAVs of the event, the mobile GCS then executes the proposed energy-aware multi-UAV dispatch algorithm (EAMUD) to dispatch multiple UAVs to this disaster area for building the FANET. Hence, the broken-down link in the disaster area is recovered after the FANET connects to nearby network infrastructure. Further, we propose the multi-UAV handoff scheme and exception handling processes to replace energy-exhausted UAVs for maximizing the event communication time of the disaster event. Finally, we execute simulations for related work and four EAMUD variants under different parameter values in the real scenario. These results exhibit that EAMUD with the Postpone method (EAMUD-P) achieves the highest event communication time among all these schemes.