This paper describes an adaptive control for nonholonomic mobile robots, which are subjected to a suddenly changed disturbance due to the change of payloads. We adopts a control architecture based on a two-degrees-of-freedom design, where the feedforward controller is constructed by a neural network (NN) to acquire an inverse dynamical model of the robot, whereas the feedback controller is designed by two methods: one is a conventional PD compensator and the other is an adaptive fuzzy compensator. A concept of virtual master-slave robots is applied to obtain an inverse model of a nonholonomic robot. A compensator needs to be used to reduce the effect of the NN mapping errors or to suppress the effect of a sudden change of payloads. It is demonstrated by several simulations that the present approach Is effective for controlling a nonholonomic mobile robot in a navigation of trajectory tracking problem for the positions and azimuth.