Type 2 diabetes (T2D) is a chronic condition that can lead to significant harm, such as heart disease, kidney disease, nerve damage, and blindness. Although T2D-related genes have been identified through Genome-wide association studies (GWAS) and various computational methods, the biological mechanism of T2D at the cell type level remains unclear. Exploring cell type-specific genes related to T2D is essential to understand the cellular mechanisms underlying the disease. To address this issue, we introduce DiGCellNet (predicting Disease Genes with Cell type specificity based on biological Networks), a model that integrates graph convolutional network (GCN) and multi-task learning (MTL) to predict T2D-associated cell type-specific genes based on the biological network. Our work represents the first attempt to predict cell type-specific disease genes using GCN and MTL. We evaluate our approach by predicting genes specific to four cell types and demonstrate that the proposed DiGCellNet outperforms other models that combine node embeddings with traditional machine learning algorithms. Moreover, DiGCellNet successfully identifies CALM1 as a gene specific to beta cell type in T2D cases, and this association is confirmed using an independent dataset. The code is available at https://github.com/23AIBox/23AIBox-DiGCellNet.Copyright © 2023 Elsevier Ltd. All rights reserved.