An unmanned aerial vehicle (UAV)-aided secure communication system is conceived and investigated, where the UAV transmits legitimate information to a ground user in the presence of an eavesdropper (Eve). To guarantee the security, the UAV employs a power splitting approach, where its transmit power can be divided into two parts for transmitting confidential messages and artificial noise (AN), respectively. We aim to maximize the average secrecy rate by jointly optimizing the UAVs trajectory, the transmit power levels and the corresponding power splitting ratios allocated to different time slots during the whole flight time, subject to both the maximum UAV speed constraint, the total mobility energy constraint, the total transmit power constraint, and other related constraints. To efficiently tackle this non-convex optimization problem, we propose an iterative algorithm by blending the benefits of the block coordinate descent (BCD) method, the concave-convex procedure (CCCP) and the alternating direction method of multipliers (ADMM). Specially, we show that the proposed algorithm exhibits very low computational complexity and each of its updating steps can be formulated in a nearly closed form. Our simulation results validate the efficiency of the proposed algorithm.