An approach for the on-line synthesis of wavelet network using recursive least square (RLS) training is proposed. It is based on the concept of successive approximation of the system function to be learned. By using the Bayesian Information Criteria (BIC), the optimal number of wavelets is determined in the training process. Simulation results show that the proposed approach can approximate the unknown system function satisfactorily. Moreover, it can adapt to the changes in system parameters that off-line training cannot.