In this paper, an self-organizing neural-network-based adaptive control (SONNAC) system is developed. The SONNAC system is comprised of a neural controller and a compensation controller. The neural controller utilizes a self-organizing neural network (SONN) to mimic an ideal controller, and the compensation controller is designed to compensate for the approximation error between the neural controller and the ideal controller. When the approximation performance of the SONN is not good enough, the SONN can create new neurons in the hidden layer to decrease the approximation error. Moreover, the adaptive laws of controller parameters are derived in the sense of Lyapunov, so that the stability of the system can be guaranteed. Finally, to investigate the effectiveness of the proposed SONNAC system, the design methodology is applied to control a linear ultrasonic motor.