A new adaptive beamforming technique based on neural networks (NNs) is proposed. The NN training is accomplished by applying a novel optimization method called Mutated Boolean PSO (MBPSO). In the beginning of the procedure, the MBPSO is repeatedly applied to a set of random cases to estimate the excitation weights of an antenna array that steer the main lobe towards a desired signal, place nulls towards several interference signals and achieve the lowest possible value of side lobe level. The estimated weights are used to train effciently a NN. Finally, the NN is applied to a new set of random cases and the extracted radiation patterns are compared to respective patterns extracted by the MBPSO and a well-known robust adaptive beamforming technique called Minimum Variance Distortionless Response (MVDR). The aforementioned comparison has been performed considering uniform linear antenna arrays receiving several interference signals and a desired one in the presence of additive Gaussian noise. The comparative results show the advantages of the proposed technique.