Tracking variations in both the latency and amplitude of evoked potential (EP) is important in quantifying properties of the nervous system. Adaptive filtering is a powerful tool for tracking such variations. In this paper, a data-reusing nonlinear adaptive filtering method, based on a radial basis function network (RBFN), is implemented to estimate EP. The RBFN consists of an input layer of source nodes, a single hidden layer of nonlinear processing units and an output layer of linear weights. It has built-in nonlinear activation functions that allow learning of function mappings. Moreover, it produces satisfactory estimates of signals against a background noise without a priori knowledge of the signal, provided that the signal and noise are independent. In clinical situations where EP responses change rapidly, the convergence rate of the algorithm becomes a critical factor. A carefully designed data-reusing RBFN can accelerate the convergence rate markedly and, thus, enhance its performance. Both theoretical analysis and simulation results support the improved performance of our new algorithm.