Heart failure has become a huge public health problem, and failure to accurately predict readmission will further lead to the disease’s high cost and high mortality. The construction of readmission prediction model can assist doctors in making decisions to prevent patients from deteriorating and reduce the cost burden. This paper extracts the patient discharge records from the MIMIC-III database. It divides the patients into three research categories: no readmission, readmission within 30 days, and readmission after 30 days, to predict the readmission of patients. We propose the HR-BGCN model to predict the readmission of patients. First, we use the Adaptive-TMix to improve the prediction indicators of a few categories and reduce the impact of unbalanced categories. Then, the knowledge-informed graph attention mechanism is proposed. By introducing a document-level explicit diagram structure, the coding ability of graph node features is significantly improved. The paragraph-level representation obtained through graph learning is combined with the context token-level representation of BERT, and finally, the multi-classification task is carried out. We also compare several typical graph learning classification models to verify the model’s effectiveness, such as the IA-GCN model, GAT model, etc. The results show that the average F1 score of the HR-BGCN model proposed in this paper for 30-day readmission of heart failure patients is 88.26%, and the average accuracy is 90.47%. The HR-BGCN model is significantly better than the graph learning classification model for predicting heart failure readmission. It can help doctors predict the 30-day readmission of patients, then reduce the readmission rate of patients.