Unmanned aerial vehicle (UAV) wireless communication has recently been recognized to be inevitable and prevalent in the fifth-generation (5G) wireless networks. In this paper, we propose a secure transmission scheme for a wiretap channel, where a source communicates with a legitimate UAV in the presence of an eavesdropper. We consider the full-duplex active eavesdropper, which performs both eavesdropping and malicious jamming simultaneously. The source transmits artificial noise (AN) signals, in addition to information signals, to confuse this eavesdropper. By considering the ground-To-UAV channel model, we analyze the hybrid outage probability, which takes both the transmission outage probability and the secrecy outage probability into consideration. We further provide the asymptotic hybrid outage probability in a more compact form, where both the transmit power at the source and the jamming power at the eavesdropper become large with a fixed ratio. Through the analysis and the numerical results, we determine the optimal power allocation factor between information signals and AN signals as well as the operating height of UAV that minimize the hybrid outage probability. We also provide the most harmful antenna configuration of the eavesdropper to the UAV communications, and this paper can be a useful framework for the design of confidential UAV communication system.