Unmanned aerial vehicles (UAVs) have emerged as a promising technology to provide low-latency mobile edge computing (MEC) services. To fully utilize the potential of UAV-assisted MEC in practice, both technical and economic challenges need to be addressed: how to optimize UAV trajectory for online task offloading and incentivize the participation of UAVs without compromising the privacy of user equipment (UE). In this work, we consider unique features of UAVs, i.e., high mobility as well as limited energy and computing capacity, and propose privacy-preserving auction frameworks, Ptero, to schedule offloading tasks on the fly and incentivize UAVs’ participation. Specifically, Ptero first decomposes the online task offloading problem into a series of one-round problems by scaling the UAV’s energy constraint into the objective. To protect UE’s privacy, Ptero calculates UAV’s coverage based on subset-anonymity. At each round, Ptero schedules UAVs greedily, computes remuneration for working UAVs, and processes unserved tasks in the cloud to maximize the system’s utility (i.e., minimize social cost). Theoretical analysis proves that Ptero achieves truthfulness, individual rationality, computational efficiency, privacy-preserving and a nontrivial competitive ratio. Trace-driven evaluations further verify that Ptero can reduce the social cost by up to 116% compared with four state-of-the-art algorithms.