Unmanned aerial vehicles (UAVs) have been emerged as cost-effective platforms to extend the coverage of mobile edge computing (MEC) system. However, the broadcast and line-of-sight (LoS) channels in UAV communications create opportunities for malicious eavesdroppers to intercept the offloaded information from ground users, posing a serious challenge to both communication and computing security. In this correspondence, we investigate the problem of secure transmission in UAV-aided MEC systems. Our goal is to maximize the average secure computing capacity by jointly designing the UAV trajectory, time allocation and offloading decision strategy. To this end, we propose a novel double-deep Q-learning (DDQN) based trajectory optimization and resource allocation scheme. Furthermore, the size of the original action space is reduced to boost the convergence of the proposed DDQN-based scheme. Additionally, we design a reward function to navigate the UAV towards its intended destination. Simulation results demonstrate that the proposed DDQN-based scheme outperforms the baselines in terms of average secure computing capacity.