The prediction of RNA secondary structures is essential for understanding its underlying principles and applications in diverse fields, including molecular diagnostics and RNA-based therapeutic strategies. However, the complexity of the search space presents a challenge. This work proposes a Graph Convolutional Network (GCNfold) for predicting the RNA secondary structure. GCNfold considers an RNA sequence as graph-structured data and predicts posterior base-pairing probabilities given the prior base-pairing probabilities, calculated using McCaskill’s partition function. The performance of GCNfold surpasses that of the state-of-the-art folding algorithms, as we have incorpo-rated minimum free energy information into the richly parameterized network, enhancing its robustness in predicting non-homologous RNA secondary structures. A Symmetric Argmax Post-processing algorithm ensures that GCNfold formulates valid structures. To validate our algo-rithm, we applied it to the SARS-CoV-2 E gene and determined the secondary structure of the E-gene across the Betacoronavirus subgenera.