Since the unmanned aerial vehicle (UAV) has high maneuverability and simple deployment, the UAV-based transmission technology has received much attention. As an important resource of the communication system, power allocation will affect the each link performance and the energy efficiency. In this paper, taking the energy efficiency as a criterion, a power allocation algorithm is proposed for UAV relay communication system under rician fading channel. First, the problem of power allocation is formulated as an optimization model for amplify-and-forward (AF) relay transmission model. Then the beamforming optimization scheme is obtained with the fixed transmission power. Next, the original non-convex optimization problem is transformed into convex optimization problem through large signal to noise ratio interval approximation. Finally, Karush-Kuhn-Tucker (KKT) condition is used to calculate the closed form of the optimal power allocation. Simulation results show that the performance of proposed algorithm is very close to that of the iterative method. But the computational complexity is lower. Compared with the average algorithm, the proposed algorithm has more larger energy efficiency which can lead to system performance improvement.