Bandwidth resources are crucial for the internal communication and task execution of multi-UAV systems. However, traditional allocation models for multi-UAV system are inefficient and result in low utility of UAVs. To overcome this challenge, this paper proposes a novel bandwidth-oriented task allocation model that accounts for the supply-demand relationship between UAVs and tasks for bandwidth resources. To solve this model, this paper presents a Double Auction-based Task Allocation Mechanism, which can achieve distributed allocation of tasks and bandwidth among multi-UAV. The main steps of this mechanism are as follows: (1) each UAV privately submits its bandwidth demand and bids for each task; (2) each task determines the bandwidth price and initial allocation based on the bids, and announces them to each UAV; (3) each UAV selects the task that maximizes its utility, and obtains the final allocation. Furthermore, this paper proves that this mechanism satisfies desirable economic properties such as individual rationality, budget balance, and incentive compatibility. Finally, experimental results show that the proposed mechanism exhibits excellent performance in terms of UAV and task utility, as well as the rate of bandwidth allocation.