Dysregulation of gene expression in Alzheimer's disease (AD) remains elusive, especially at the cell type level. Gene regulatory network, a key molecular mechanism linking transcription factors (TFs) and regulatory elements to govern gene expression, can change across cell types in the human brain and thus serve as a model for studying gene dysregulation in AD. However, AD-induced regulatory changes across brain cell types remains uncharted. To address this, we integrated single-cell multi-omics datasets to predict the gene regulatory networks of four major cell types, excitatory and inhibitory neurons, microglia and oligodendrocytes, in control and AD brains. Importantly, we analyzed and compared the structural and topological features of networks across cell types and examined changes in AD. Our analysis shows that hub TFs are largely common across cell types and AD-related changes are relatively more prominent in some cell types (e.g., microglia). The regulatory logics of enriched network motifs (e.g., feed-forward loops) further uncover cell type-specific TF-TF cooperativities in gene regulation. The cell type networks are also highly modular and several network modules with cell-type-specific expression changes in AD pathology are enriched with AD-risk genes. The further disease-module-drug association analysis suggests cell-type candidate drugs and their potential target genes. Finally, our network-based machine learning analysis systematically prioritized cell type risk genes likely involved in AD. Our strategy is validated using an independent dataset which showed that top ranked genes can predict clinical phenotypes (e.g., cognitive impairment) of AD with reasonable accuracy. Overall, this single-cell network biology analysis provides a comprehensive map linking genes, regulatory networks, cell types and drug targets and reveals cell-type gene dysregulation in AD.