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In this paper, we propose a mobile edge computing (MEC)-enabled unmanned aerial vehicle (UAV)-assisted vehicular ad hoc network (VANET) architecture, based on which a number of vehicles are served by UAVs equipped with computation resource. Each vehicle has to offload its computing tasks to the proper MEC server on the UAV due to the limited computation ability. To counter the problems above, we first model and analyze the transmission model and the security assurance model from the vehicle to the MEC server on UAV, and the task computation model of the local vehicle and the edge UAV. Then, the vehicle offloading problem is formulated as a multi-objective optimization problem by jointly considering the task offloading, the resource allocation, and the security assurance. For tackling this hard problem, we decouple the multi-objective optimization problem as two subproblems and propose an efficient iterative algorithm to jointly make the MEC selection decision based on the criteria of load balancing and optimize the offloading ratio and the computation resource according to the Lagrangian dual decomposition. Finally, the simulation results demonstrate that our proposed scheme achieves significant performance superiority compared with other schemes in terms of the successful task processing ratio and the task processing delay.