Background: As noncoding RNAs, circular RNAs (circRNAs) can act as microRNA (miRNA) sponges due to their abundant miRNA binding sites, allowing them to regulate gene expression and influence disease development. Accurately identifying circRNA–miRNA associations (CMAs) is helpful to understand complex disease mechanisms. Given that biological experiments are time consuming and labor intensive, alternative computational methods to predict CMAs are urgently needed. Results: This study proposes a novel computational model named CMAGN, which incorporates several advanced computational methods, for predicting CMAs. First, similarity networks for circRNAs and miRNAs are constructed according to their sequences. Graph attention autoencoder is then applied to these networks to generate the first representations of circRNAs and miRNAs. The second representations of circRNAs and miRNAs are obtained from the CMA network via node2vec. The similarity networks of circRNAs and miRNAs are reconstructed on the basis of these new representations. Finally, network consistency projection is applied to the reconstructed similarity networks and the CMA network to generate a recommendation matrix. Conclusion: Five-fold cross-validation of CMAGN reveals that the area under ROC and PR curves exceed 0.96 on two widely used CMA datasets, outperforming several existing models. Additional tests elaborate the reasonability of the architecture of CMAGN and uncover its strengths and weaknesses.