This paper studies a multiple unmanned aerial vehicle (UAV) relaying communication system, where multiple UAV re-lays assist the blocked communication between a group of ground users (GUs) and a base station (BS). Since the UAVs only have limited-energy in practice, our design aims to maximize the energy efficiency (EE) through jointly designing the communica-tion scheduling, the transmit power allocation, as well as UAV trajectory under the buffer constraint over a given flight period. Actually, the formulated fractional optimization problem is diffi-cult to be solved in general because of non-convexity. To re-solve this difficulty, an efficient iterative algorithm is proposed based on the block coordinate descent (BCD) and successive convex approximation (SCA) techniques, as well as the Dinkel-bach 's algorithm. Specifically, the optimization variables of the formulated problem are divided into three blocks and we alter-nately optimize each block of the variables over iteration. Numeri-cal results verify the convergence of the proposed iterative al-gorithm and show that the proposed designs achieve significant EE gain, which outperform other benchmark schemes.