Thanks to excellent mobility and high probability of a Line-of-Sight (LoS) to ground objects, unmanned aerial vehicles (UAVs) have been widely used in surveillance. This paper considers the use of UAVs to covertly and collaboratively eavesdrop on suspicious wireless transmitters on the ground. We focus on the trajectory planning of the UAVs. To avoid the UAVs being visually noticed by the ground transmitters, we propose a new measure to quantify the disguising performance of the UAVs. The trajectories of the UAVs are planned to maximize the disguising performance, subject to an uninterrupted eavesdropping requirement, UAV collision avoidance and UAV aeronautic maneuverability. A new randomized method based on the Rapidly-exploring Random Tree (RRT) is developed to efficiently construct the trajectories of the UAVs. Computer simulations confirm that the proposed method outperforms the random movement method in eavesdropping performance, while achieving with comparable disguising performance.