After disasters, communication infrastructures in disaster-affected areas may fail due to physical damages or power outages. Unmanned aerial vehicles (UAVs) can act as flying base stations to satisfy the communication requirements of people in disaster-affected areas. For the purpose of increasing the data transmission rate and saving energy consumption of wireless telecommunication terminals (WTs), UAV mobility can be exploited to provide good channel conditions between UAVs and WTs. In this paper, a UAV with path length limitation is considered to provide communication service to WTs in a disaster area, a part of WTs can communicate with the UAV directly, and other WT communication with the UAV indirectly through D2D relay transmissions to reduce the UAV path length. Aiming at decreasing the total energy consumption of WTs, a novel UAV-aided data communicate method, ECO-UDC, is introduced. Extensive simulations demonstrate that ECO-UDC can reduce the energy consumption of WTs by approximately 30%-40% compared to the benchmark method.