For real-time wireless networks with strict latency and energy constraints, deep neural networks have been used to approximate the resource allocation solutions that are previously obtained by advanced but computationally expensive optimization algorithms. In this paper, we consider the multi-user beamforming design problem for sum rate maximization in multi-antenna interference channels. Specifically, we propose a gradient projection inspired recurrent neural network for efficient beamforming optimization. The key ingredient is to explore the structure of the gradient vector of the sum rate so that the network learns only a set of dimension reduced coefficients. Furthermore, we extend it to the robust beamforming design for worst-case sum rate maximization in the presence of bounded channel errors. Numerical results show that the proposed learning networks can achieve high accuracy of the sum rates while with significantly reduced runtime.