To deal with the deficiencies in load balancing and execution efficiency of existing algorithms for cooperative multi-task assignment of multi-Unmanned Aerial Vehicle （UAV）， an Improved Self-Organizing Map （ISOM） algorithm was proposed. In the algorithm， the load balancing degree of UAVs was designed according to the flight time and task execution time in order to improve the efficiency of the task completion. And a novel non-linearly changing learning rate and neighborhood function were designed to ensure the stability and fast convergence of ISOM algorithm. Then， the validity of ISOM algorithm was verified in different task environments. Experimental results show that compared with Particle Swarm Optimization combined with Genetic Algorithm （GA-PSO）， Gurobi and ORTools algorithms， the proposed algorithm has the task completion time reduced by 15.5%， 12.7% and 7.3% respectively. When the effectiveness of track length reduction was verified on KroA100， KroA150， and KroA200 examples of TSPLIB dataset， comparison results with Invasive Weed Optimization （IWO） algorithm， Improved Partheno Genetic Algorithm （IPGA） and Ant Colony-Partheno Genetic Algorithm （AC-PGA） show that ISOM algorithm has the minimum track length when the number of UAVs is 2， 3， 4， 5， 8. It can be seen that ISOM algorithm has a significant effect on solving the problem of multi-UAV cooperative multi-task assignment.