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An adaptive output feedback controller is presented for a class of single-input-single-output (SISO) nonlinear systems preceded by an unknown hysteresis nonlinearity represented by the Preisach model. First, a novel model is developed to represent the hysteresis characteristic in order to handle the case where the hysteresis output is not directly measured. The model is motivated by the Preisach model but implemented by the neural networks (NN). Therefore, it is easily used for controller design. Then, a radius-basis-functional-neural-networks (RBF NN) adaptive controller based on the model estimation is presented by combining the high-gain state observer. The updated laws and control laws of the controller are derived from Lyapunov stability theorem, so that the ultimate boundedness of the closed-loop system is guaranteed. At last, an example is used to verify the effectiveness of the controller.