The multi-UAV cooperative task allocation problem is central to multi-UAV cooperative combat. To enhance operational efficiency, this paper establishes a multi-UAV cooperative task allocation model. The model considers the constraints such as the ability of UAV and task priority, and takes the shortest total distance and task execution time of UAV swarm to complete the task as the optimization goal. A fish swarm auction hybrid algorithm is proposed to solve the model. Initially, the auction algorithm provides an allocation scheme to initialize the fish swarm algorithm, enhancing early convergence speed. Then, an adaptive improvement strategy is proposed for the step size of artificial fish. Initially, the step size is increased to enhance global search and speed up iterations. Later, it is reduced to avoid getting trapped in local optima and improve solution accuracy. The simulation results indicate that the hybrid algorithm demonstrates superior convergence and effectiveness.