Edge computing is a new computing paradigm which distributes tasks to edge networks for processing, it provides effective support for various mobile applications to meet their rapid response requirement. Unmanned Aerial Vehicle (UAV) has been widely used in emergency rescue, mapping, etc., with the advantages of flexible deployment and rapid movement. However, on one hand, mobile applications will be terminated when the battery energy is exhausted. On the other hand, mobile applications will be out of service when mobile devices are out of radio coverage of UAVs. How to achieve low-cost task unloading in the resource limited and location sensitive multi-UAVs edge computing environment is rather challenging. In this paper, we propose a distributed location-aware task offloading scheme, aiming at the above issues. Specifically, we create a nonlinear task allocation problem by combining the limited energy constraints of edge nodes with the random movement of users, where the cost function is divided into static and dynamic costs, respectively. Then, we formulate this problem to a convex optimization one with linear constrains, based on regularization technology. The mathematical proof shows that the scheme can support a parameterized competitive ratio without requiring any prior knowledge of the input task. The simulation results show that the proposed scheme can achieve lower cost edge computing services.INDEX TERMS convex programming,edge computing,task allocation,UAV