Abstract Motivation Protein–RNA interactions play essential roles in many biological processes, including pre-mRNA processing, post-transcriptional gene regulation and RNA degradation. Accurate identification of binding sites on RNA-binding proteins (RBPs) is important for functional annotation and site-directed mutagenesis. Experimental assays to sparse RBPs are precise and convincing but also costly and time consuming. Therefore, flexible and reliable computational methods are required to recognize RNA-binding residues. Results In this work, we propose PST-PRNA, a novel model for predicting RNA-binding sites (PRNA) based on protein surface topography (PST). Taking full advantage of the 3D structural information of protein, PST-PRNA creates representative topography images of the entire protein surface by mapping it onto a unit spherical surface. Four kinds of descriptors are encoded to represent residues on the surface. Then, the potential features are integrated and optimized by using deep learning models. We compile a comprehensive non-redundant RBP dataset to train and test PST-PRNA using 10-fold cross-validation. Numerous experiments demonstrate PST-PRNA learns successfully the latent structural information of protein surface. On the non-redundant dataset with sequence identity of 0.3, PST-PRNA achieves area under the receiver operating characteristic curves (AUC) value of 0.860 and Matthew’s correlation coefficient value of 0.420. Furthermore, we construct a completely independent test dataset for justification and comparison. PST-PRNA achieves AUC value of 0.913 on the independent dataset, which is superior to the other state-of-the-art methods. Availability and implementation The code and data are available at https://www.github.com/zpliulab/PST-PRNA. A web server is freely available at http://www.zpliulab.cn/PSTPRNA. Supplementary information Supplementary data are available at Bioinformatics online.