Evoked potentials are widely used to diagnose diseases and disorders in the central nervous system. It is thus essential to develop fast algorithms which can track the variations of evoked potentials for a variety of clinical applications. The background noise in evoked potentials may present an impulsive characteristic which is far from Gaussian but suitable to be modeled by the a-stable distribution. For such environments, this study derives an adaptive estimator modeled by the radial basis function neural network with the least mean ^-norm criterion for evoked potentials. However, its performance may degrade when the a value dynamically changes. To overcome this drawback, this study proposes an adaptive algorithm that uses a non-linear transform in the weight updating formula expressed in matrix form. The algorithm can track the underlying evoked potentials well, trial-by-trial, without the need to estimate the a value on-line and without a reference that depends on a priori knowledge. Simulations and experiments on human visual evoked potentials and event-related potentials are carried out to examine the performance of the proposed approach. Both theoretical analysis and experimental results show that the method can improve both estimation accuracy and convergence speed without significantly increasing computational time. Hence, the adaptive estimator for evoked potentials is robust under an impulsive noise environment.