Unmanned Aerial Vehicles (UAVs) have been regarded as a promising means to reshape future wireless communication systems. In this paper, we consider how to plan the trajectory of a solar-powered UAV under a cloudy condition to secure the communication between the UAV and a target ground node against multiple eavesdroppers. We propose a new 3D UAV trajectory optimization model by taking into account the UAV energy consumption, solar power harvesting, eavesdropping and no-fly zone avoidance. A Rapidly-exploring Random Tree (RRT) method is developed to construct the UAV trajectory. Computer simulations and comparisons with a baseline method demonstrate that the proposed method is able to produce trajectories to ensure the valid wireless communication link with the ground node and prevent eavesdropping.