A new antenna array beamformer based on neural networks (NNs) is presented. The NN training is performed by using optimized data sets extracted by a novel invasive weed optimization (IWO) variant called modified adaptive dispersion IWO (MADIWO). The trained NN is utilized as an adaptive beamformer that makes a uniform linear antenna array steer the main lobe toward a desired signal, place respective nulls toward several interference signals, and suppress the side lobe level (SLL). Initially, the NN structure is selected by training several NNs of various structures using MADIWO-based data and by making a comparison among the NNs in terms of training performance. The selected NN structure is then used to construct an adaptive beamformer, which is compared to MADIWO-based and ADIWO-based beamformers, regarding the SLL and the ability to properly steer the main lobe and the nulls. The comparison is made, considering several sets of random cases with different numbers of interference signals and different power levels of additive zero-mean Gaussian noise. The comparative results exhibit the advantages of the proposed beamformer.