Kidney transplantation (KT) is associated with improved health outcomes for patients with end-stage kidney disease; therefore, matching donors to recipients to optimize health outcomes for recipients is important. This study leverages Graph Neural Networks (GNNs) to improve donor-recipient matching (DRM) in KT by embedding bipartite heterogeneous graph nodes into a shared feature space for compatibility prediction. We developed a kidney transplant graph using donor and recipient data and domain knowledge. Using the kidney transplant graph, we pursue DRM by predicting compatibility edges—i.e. edges from a donor to an optimal recipient (alive at 5 years post-transplant without graft failure). Using GraphSAGE, we trained and evaluated our GNN model on a dataset of kidney transplant recipients from 2000 to 2014, including 27k nodes and 49M edges. The proposed GNN model achieved an F1-score of 0.74 and an AUC of 0.77 for 5-year all-cause graft survival, outperforming traditional models like XGBoost and random forest. By incorporating neighborhood information, our GNN demonstrated the potential to identify mislabeled samples, enhance prediction accuracy, and advance machine learning applications in KT.