The RNA-binding site on a protein consists of the amino acid residues that directly interact with RNA. Identification of RNA-binding sites on the proteins is key to understanding various post-transcriptional regulations. To determine RNA-binding sites using experimental methods has the limitations of high costs and low throughput. Computational methods offer an attractive alternate solution. Despite the many successes that have been claimed by various research groups, current computational methods still suffer relatively low accuracy in independent tests. Therefore, there is an urging need to develop better computational methods. In this study, we applied a deep learning method, namely concurrent neural network (CNN), to identify RNA-binding residues on the proteins. In a five-fold cross validation, the CNN achieved an accuracy of 97.2% with 0.98 area under curve (AUC). Comparisons shows that the deep learning method is superior to other state-of-the-art machine learning methods, including support vector machine and Random Forest.