Wavelet neural networks (WNN) have recently attracted great interest, because of their advantages over radial basis function networks (RBFN) as they are universal approximators but achieve faster convergence and are capable of dealing with the so-called "curse of dimensionality." In addition, WNN are generalized RBFN. However, the generalization performance of WNN trained by least-squares approach deteriorates when outliers are present. In this paper, we propose a robust wavelet neural network based on the theory of robust regression for dealing with outliers in the framework of function approximation. By adaptively adjusting the number of training data involved during training, the efficiency loss in the presence of Gaussian noise is accommodated. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed network.