With the development of the Internet of Things (IoT), Unmanned Aerial Vehicle-Mobile Edge Computing (UAV-MEC) plays a critical role in enhancing network performance and data processing capabilities. However, significant challenges that impede system performance in UAV-MEC systems include task scheduling inefficiency, privacy leakage, and insufficient trust evaluation. To address these issues, we propose a novel framework that synergistically integrates a UAV trust evaluation model, Differential Privacy Federated Learning (DPFL), and the Deep Deterministic Policy Gradient (DDPG) algorithm. The core innovation lies in creating a security-aware DRL agent, where the trust model guides the DDPG’s decisions to inherently balance efficiency with security, while the entire collaborative learning process is protected by DPFL. By incorporating trust evaluation and privacy protection mechanisms, the proposed method achieves secure task scheduling with minimal latency under the condition of high trust values, while considering UAV energy constraints and successfully optimizing UAV trajectories. Simulation results demonstrate that, compared to traditional Deep Reinforcement Learning (DRL) algorithms, the proposed algorithm significantly reduces the cost by 4.12% and exhibits higher stability and convergence. Specifically, under varying conditions such as user counts, random task sizes, UAV computational capacities, and levels of UAV intrusion power, the costs decreased by up to 9.56%, 5.49%, 3.77%, and 4.43%, respectively. Overall, the proposed scheme exhibits significant improvements in user privacy protection, system efficiency, and adaptability.