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• We consider a new optimization problem for dual UAVs that one UAV is utilized as a mobile wireless relay and the other auxiliary UAV is used to interfere with the eavesdropper. Here, the eavesdropper whose actual position is unknown attempts to eavesdrop on information illegally. • We formulate a critical problem that how to maximize the average secrecy rate with the constraints of trajectories and transmit power of dual UAVs as well as the information causality. This optimization problem is thorny because of the characteristic of non-convex. • We propose an iterative algorithm that jointly optimize the trajectories and transmit power for dual UAVs with multiple constraints. We decompose the original problem into three tractable subproblems by applying the successive convex approximation technique. Then, we alternately optimize the trajectories and transmit power for dual UAVs through a method of block coordinate descent to make the average secrecy rate maximized. Unmanned aerial vehicles (UAVs) face a lot of security challenges due to the openness of their wireless communication. In this paper, we investigate how to improve the security of wireless communication when the UAV is utilized as a wireless relay. We consider a new scenario where the dual UAVs are employed cooperatively to transmit confidential information and an eavesdropper whose actual position is unknown attempts to eavesdrop on the information illegally. We propose an optimization problem for the average secrecy rate under multiple constraints. The optimization problem we proposed is non-convex and complicated. We design an iterative algorithm that jointly optimizes the trajectories and transmit power to make the average secrecy rate maximized via the block coordinate descent and successive convex approximation techniques. The feasibility of this method is verified by numerical simulation. [ABSTRACT FROM AUTHOR]