In this paper, a neural network approach to task assignment, based on a self-organizing map (SOM), is proposed for a multirobot system in dynamic environments subject to uncertainties. It is capable of dynamically controlling a group of mobile robots to achieve multiple tasks at different locations, so that the desired number of robots will arrive at every target location from arbitrary initial locations. In the proposed approach, the robot motion planning is integrated with the task assignment, thus the robots start to move once the overall task is given. The robot navigation can be dynamically adjusted to guarantee that each target location has the desired number of robots, even under uncertainties such as when some robots break down. The proposed approach is capable of dealing with changing environments. The effectiveness and efficiency of the proposed approach are demonstrated by simulation studies.