Achieving robust and fast two-dimensional adaptive beamforming of phased array antennas is a challenging problem due to its high-computational complexity. To address this problem, a deep-learning-based beamforming method is presented in this paper. In particular, the optimum weight vector is computed by modeling the problem as a convolutional neural network (CNN), which is trained with I/O pairs obtained from the optimum Wiener solution. In order to exhibit the robustness of the new technique, it is applied on an 8 × 8 phased array antenna and compared with a shallow (non-deep) neural network namely, radial basis function neural network. The results reveal that the CNN leads to nearly optimal Wiener weights even in the presence of array imperfections.