This paper presents a recurrent neural network (RNN)-based speech enhancement method for a binaural hearing aid system. We design a binaural RNN architecture to train gains of subbands. The proposed method trains the binaural recurrent neural network from binaural signals separately before concatenating to a weighting fully connected layer. The method preserves more cues from binaural signals using different training strategies and weighting variations. The results show the proposed method achieves a balance between speech intelligence and noise suppression in different acoustics scene. We demonstrate that the proposed method can implement speech enhancement for hearing aids with a low complexity neural network. This makes it applicable on smartphone or embedded devices.