The explosive computation demands in the Internet of Things (IoT) have triggered the research interests on unmanned aerial vehicle (UAV) assisted mobile-edge computing (MEC) systems even though there are still many challenges, such as computing delay requirement, multi-UAV cooperation, and resource management. This letter focuses on the computing delay issue in MEC systems assisted by multiple UAVs with the goal of task completion time minimization. In particular, both the partial offloading and binary offloading modes are considered by jointly optimizing time slot size, terminal devices scheduling, computation resource allocation, and UAVs’ trajectories. Particularly, an non-LoS channel model is adopted for UAV-ground communication. To handle the formulated problems, we develop alternating optimization algorithms by invoking the successive convex approximation method, Karush-Kuhn-Tucker conditions and penalized method. Numerical results show that the completion time is significantly decreased by the proposed algorithms.