Circular RNAs (circRNAs), with their crucial roles in gene regulation and disease development, have become rising stars in the RNA world. To understand the regulatory function of circRNAs, many studies focus on the interactions between circRNAs and RNA-binding proteins (RBPs). Recently, the abundant CLIP-seq experimental data has enabled the large-scale identification and analysis of circRNA–RBP interactions, whereas, as far as we know, no computational tool based on machine learning has been proposed yet. We develop CRIP (CircRNAs Interact with Proteins) for the prediction of RBP-binding sites on circRNAs using RNA sequences alone. CRIP consists of a stacked codon-based encoding scheme and a hybrid deep learning architecture, in which a convolutional neural network (CNN) learns high-level abstract features and a recurrent neural network (RNN) learns long dependency in the sequences. We construct 37 data sets including sequence fragments of binding sites on circRNAs, and each set corresponds to an RBP. The experimental results show that the new encoding scheme is superior to the existing feature representation methods for RNA sequences, and the hybrid network outperforms conventional classifiers by a large margin, where both the CNN and RNN components contribute to the performance improvement.