In this paper, we investigate the use of prediction-adaptation-correction recurrent neural networks (PAC-RNNs) for low-resource speech recognition. A PAC-RNN is comprised of a pair of neural networks in which a {\it correction} network uses auxiliary information given by a {\it prediction} network to help estimate the state probability. The information from the correction network is also used by the prediction network in a recurrent loop. Our model outperforms other state-of-the-art neural networks (DNNs, LSTMs) on IARPA-Babel tasks. Moreover, transfer learning from a language that is similar to the target language can help improve performance further.