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In this paper, an Unmanned Aerial Vehicle (UAV)-assisted relay communication system is studied, where a UAV is served as a flying relay to maintain a communication link between a mobile source node and a remote destination node. Specifically, an average outage probability min-imization problem is formulated firstly, with the constraints on the transmission power of the source node, the maximum energy consumption budget, the transmission power, the speed and accelera-tion of the flying UAV relay. Next, the closed-form of outage probability is derived, under the hybrid line-of-sight and non-line-of-sight probability channel model. To deal with the formulated nonconvex optimization, a long-term proactive optimization mechanism is developed. In particular, firstly, an approximation for line-of-sight probability and a reformulation of the primal problem are given, respectively. Then, the reformulated problem is transformed into two subproblems:one is the transmission power optimization with given UAV's trajectory and the other is the trajectory opti-mization with given transmission power allocation. Next, two subproblems are tackled via tailoring primal–dual subgradient method and successive convex approximation, respectively. Furthermore, a proactive optimization algorithm is proposed to jointly optimize the transmission power alloca-tion and the three-dimensional trajectory. Finally, simulation results demonstrate the performance of the proposed algorithm under various parameter configurations.