In this work, we consider an Unmanned Aerial Vehicle (UAV) aided covert edge computing architecture, where multiple sensors are scattered with a certain distance on the ground. The sensor can implement several computation tasks. In an emergency scenario, the computational capabilities of sensors are often limited, as seen in vehicular networks or Internet of Things (IoT) networks. The UAV can be utilized to undertake parts of the computation tasks, i.e., edge computing. While various studies have advanced the performance of UAV-based edge computing systems, the security of wireless transmission in future 6G networks is becoming increasingly crucial due to its inherent broadcast nature, yet it has not received adequate attention. In this paper, we improve the covert performance in a UAV aided edge computing system. Parts of the computation tasks of multiple ground sensors are offloaded to the UAV, where the sensors offload the computing tasks to the UAV, and Willie around detects the transmissions. The transmit power of sensors, the offloading proportions of sensors and the hovering height of the UAV affect the system covert performance, we propose a deep reinforcement learning framework to jointly optimize them. The proposed algorithm minimizes the system average task processing delay while guaranteeing that the transmissions of sensors are not detected by the Willie under the covertness constraint. Extensive simulations are conducted to verify the effectiveness of the proposed algorithm to decrease the average task processing delay with comparison with other algorithms.