Unmanned aerial vehicles (UAVs) are deployed in emergency disaster-relief operations to provide communication services as substitutes for damaged ground base stations (BSs), as well as to offload computational tasks for applications such as target recognition. In view of the limited computing power of a single UAV, we focus on the edge computing offloading problem with multiple-UAV cooperation. As a single UAV is not enough to offload massive delay-sensitive computing tasks in the emergency communication scenarios, we have built up a multi-UAV cooperation computing architecture. By exploring the multiple-UAV cooperation computing offloading capacity, we formulated an optimization problem of minimizing the total time slot size. Since the proposed problem is relevant to mixed integer nonlinear programming, it can be decomposed into two sub-problems: computing task scheduling and UAV trajectory. To handle the formulated problems, we developed a joint optimization algorithms by invoking the penalty method and successive convex approximation (SCA) method. The simulation results show that, compared with the benchmark algorithms, the proposed algorithm can significantly reduce the computation task delay and improve the execution efficiency of the UAVs.