Cancer heterogeneity makes it necessary to use different treatment strategies for patients with the same pathological features. Accurate identification of cancer subtypes is a crucial step in this approach. The current studies of pancreatic ductal adenocarcinoma (PDAC) subtypes mainly focus on single genes and ignore the synergistic effects of genes. Here we proposed a network alignment algorithm GCNA-cluster to cluster patients based on gene co-expression networks. We constructed weighted gene co-expression networks for patients and aligned the networks of two patients to estimate the similarity of patients and their cancer subtypes. A scoring function is defined to measure the network alignment result and the score can indicate the similarity between patients. Then, the patients are clustered based on their similarities. We validated the accuracy of the algorithm on the GEO-PDAC dataset with real labels, and the experimental results show that the GCNA-cluster algorithm has better results than classical cancer subtyping algorithms. In addition, the GCNA-cluster algorithm applied to the TCGA-PDAC dataset identified two subtypes based on the Silhouette Coefficient. Biomarkers identified for the PDAC subtypes hint to cell growth, cell cycle or apoptosis as targets for new therapeutic strategies.