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This paper studies a new mobile edge computing (MEC) setup where an unmanned aerial vehicle (UAV) is served by cellular ground base stations (GBSs) for computation offloading. The UAV flies between a given pair of initial and final locations, during which it needs to accomplish certain computation tasks by offloading them to some selected GBSs along its trajectory for parallel execution. Under this setup, we aim to minimize the UAV's mission completion time by optimizing its trajectory jointly with the computation offloading scheduling, subject to the maximum speed constraint of the UAV, and the computation capacity constraints at GBSs. The joint UAV trajectory and computation offloading optimization problem is, however, non-convex and thus difficult to be solved optimally. To tackle this problem, we propose an efficient algorithm to obtain a high-quality suboptimal solution. Numerical results show that the …