Abstract: The fuzzy neural network has good nonlinear function approximation properties, and wavelet transform has good time-frequency signal analysis capabilities. The single hidden layer fuzzy recurrent wavelet neural network (SLFRWNN) is developed by combining with the advantages of both in this paper. The structure of networks, the form of its activation functions and its influence on SLFRWNN are analyzed. Then a design method of adaptive observer based on the single hidden layer recurrent fuzzy wavelet neural network is proposed. The Lyapunov function is introduced to prove the stability of this observer design method. And the network observer of initialization and the optimal learning algorithm is given. The final simulation results show that the single hidden layer neural fuzzy recurrent wavelet network observer can easily observe the state of the system.