When adaptive arrays are applied to practical problems, the performances of the existing adaptive algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal. Similar types of performance degradation can occur when the signal array response is known precisely but the training sample size is small. In this paper, we propose a novel neural network approach to robust adaptive beamforming. The proposed algorithm is based on explicit modeling of uncertainties in the desired signal array response and a three-layer radial basis function neural network (RBFNN). In the proposed algorithm, the computation of the optimum weight vector is viewed as a mapping problem, which can be modeled using a RBFNN trained with input/output pairs. Our proposed approach offers fast convergence rate, provides excellent robustness against some types of mismatches and makes the mean output array SINR consistently close to the optimal one. Computer simulation results are presented, which show that the proposed algorithm yields significantly better performance as compared with the existing adaptive beamforming algorithms.