Objective Inferring cancer driver genes, especially rare or sample-specific cancer driver genes, is crucial for precision oncology. Considering the high inter-tumor heterogeneity, a few recent methods attempt to reveal cancer driver genes at the individual level. However, most of these methods generally integrate multi-omics data into a single biomolecular network (e.g., gene regulatory network or protein-protein interaction network) to identify cancer driver genes, which results in missing important interactions highlighted in different networks. Thus, the development of a multiplex network method is imperative in order to integrate the interactions of different biomolecular networks and facilitate the identification of cancer driver genes.Methods A multiplex network control method called Personalized cancer Driver Genes with Multiplex biomolecular Networks (PDGMN) was proposed. Firstly, the sample-specific multiplex network, which contains protein-protein interaction layer and gene-gene association layer, was constructed based on gene expression data. Subsequently, somatic mutation data was integrated to weight the nodes in the sample-specific multiplex network. Finally, a weighted minimum vertex cover set identification algorithm was designed to find the optimal set of driver nodes, facilitating the identification of personalized cancer driver genes.Results The results derived from three TCGA cancer datasets indicate that PDGMN outperforms other existing methods in identifying personalized cancer driver genes, and it can effectively identify the rare driver genes in individual patients. Particularly, the experimental results indicate that PDGMN can capture the unique characteristics of different biomolecular networks to improve cancer driver gene identification.Conclusion PDGMN can effectively identify personalized cancer driver genes and broaden our understanding of cancer driver gene identification from a multiplex network perspective. The source code and datasets used in this work are available at https://github.com/NWPU-903PR/PDGMN.