As an extension of centralized cloud services in a space-air-ground integrated network, an unmanned aerial vehicle (UAV-)-enabled edge network brings computation as close ground terminals of need as possible. In this scenario, the UAV is considered a mobile base station (MBS) to achieve data forwarding and processing from cloud servers to terminals. Note that downlink signals from the MBS to ground terminals are vulnerable to passive wiretapping by a malicious node. We formulate an average secrecy rate maximization problem to tackle the wiretapping issue by simultaneously transmitting confidential information and artificial noise (AN). We decompose the problem into two subproblems, including the UAV transmit power allocation subproblem and the UAV trajectory subproblem. Then, we adopt the successive convex approximation scheme and the alternating optimization method to develop our iterative algorithm to achieve secure transmission. Simulation results demonstrate that the proposed scheme is significantly better than other benchmarks in UAV-enabled downlink communication secrecy performance.