The problems of severe channel fading and limited computation capacity of a single MEC server in a traditional mobile edge computing(MEC)network are investigated.The task completion maximization scheme is proposed in an unmanned aerial vehicles(UAV)assisted multi-MEC server network.The scheme jointly optimizes task offloading decision,computation and communication resource,and UAV trajectory to formulate the task completion rate maximi-zation and the weighted energy consumption minimization problem between UAV and user,while satisfying the information causality constraint,task constraint,and trajectory constraint.In or-der to solve this problem,an alternating optimization algorithm is adopted to decouple the highly complex problem into a task offloading and resource allocation problem,as well as a UAV trajec-tory design problem.For the task offloading and resource allocation problems,the variable sub-stitution algorithm and the Lagrangian dual algorithm are used to solve the transformed convex problems iteratively.The UAV trajectory is optimized with the successive convex approximation algorithm.Simulation results show that the proposed scheme can effectively improve the task completion rate and reduce the system energy consumption,and can effectively alleviate the prob-lems of channel fading and limited computational capacity of a single MEC server.