The de novo peptide-sequencing method can be used to directly infer the peptide sequence from a tandem mass spectrum. It has the advantage of not relying on protein databases and plays a key role in the determination of the protein sequences of unknown species, monoclonal antibodies, and cancer neoantigens. In this paper, we propose a method based on graph convolutional neural networks and convolutional neural networks, Denovo-GCN, for de novo peptide sequencing. We constructed an undirected graph based on the mass difference between the spectral peaks in a tandem mass spectrum. The features of the nodes on the spectrum graph, which represent the spectral peaks, were the matching information of the peptide sequence and the mass spectrum. Next, the Denovo-GCN used CNN to extract the features of the nodes. The correlation between the nodes was represented by an adjacency matrix, which aggregated the features of neighboring nodes. Denovo-GCN provides a complete end-to-end training and prediction framework to sequence patterns of peptides. Our experiments on various data sets from different species show that Denovo-GCN outperforms DeepNovo with a relative improvement of 13.7–25.5% in terms of the peptide-level recall.