Employing unmanned aerial vehicles (UAVs) to assist conventional terrestrial communications has brought significant interest recently due to the attractive advantages of UAV communications. In this paper, the UAV is considered as a relay to support the communications between the base station and distant mobile users, where the UAV adjusts its three dimensional coordinate and transmit power to accommodate the mobility of multiple mobile users network. Our objective is to maximize the sum rate of all users, while taking into account the quality-of-service requirement of each user, the line-of-sight connections for communication links and the information-causality constraint for the relaying system. However, the considered problem is challenging to solve, because the objective function and constraint are non-convex with mutually coupled variables. Firstly, we study the UAV-supported single user relaying case, and obtain an analytical optimal solution. Next, we propose an efficient algorithm based on the concept of successive convex approximation and the structure property of the problem. Furthermore, we demonstrate simulation results to show the effectiveness of the proposed algorithm and reveal the impacts of different parameters on the system performance.