The auction algorithm is a widely used method for task assignments. However, most existing auction algorithms yield poor performance when applied to multi-UAVs dynamic task assignment. To end this, we propose a novel hybrid ''Two-Stage'' auction algorithm based on the hierarchical decision mechanism and an improved objective function, which simultaneously realizes heterogeneous multi-UAVs dynamic task assignment with limited resources of each UAV and avoidance obstacle path planning. In the first stage, according to the novel proposed hierarchical decision mechanism, we select a task that is urgently needed to be performed in the task group by using the decision function and three attribute values of tasks. After the first stage, it will result in a reasonable auction sequence, instead of random auction sequence as in previous algorithms. In the second stage, by considering the coverage factor and adaptive-limitation penalty term, a novel objective function is proposed and directs related UAVs for auction. In addition, we combine the structural advantages of the centralized and distributed auction algorithm, which greatly promotes its performance in dynamic task assignment. The experimental results demonstrate that the proposed method outperforms many state-of-the-art models in efficiency and robustness. INDEX TERMS Hierarchical decision mechanism, unmanned air vehicle, dynamic task assignment, auction algorithm, decision function.