Peanut (Arachis hypogaea L.) is an important oilseed crop worldwide. However, soil salinization becomes one of the main limiting factors of peanut production. Therefore, developing salt-tolerant varieties and understanding the molecular mechanisms of salt tolerance is important to protect peanut yield in saline areas. In this study, we selected four peanut varieties with contrasting response to salt challenges with T1 and T2 being tolerance and S1 and S2 being susceptible. High-throughput RNA sequencing resulted in more than 314.63 Gb of clean data from 48 samples. We identified 12,057 new genes, 7,971of which have functional annotations. KEGG pathway enrichment analysis of uniquely expressed genes in salt-tolerant peanut revealed that upregulated genes in the root are involved in the MAPK signaling pathway, fatty acid degradation, glycolysis/gluconeogenesis, and upregulated genes in the shoot were involved in plant hormone signal transduction and the MAPK signaling pathway. Na+ content, K+ content, K+/ Na+, and dry mass were measured in root and shoot tissues, and two gene co-expression networks were constructed based on weighted gene co-expression network analysis (WGCNA) in root and shoot. In this study, four key modules that are highly related to peanut salt tolerance in root and shoot were identified, plant hormone signal transduction, phenylpropanoid biosynthesis, starch and sucrose metabolism, flavonoid biosynthesis, carbon metabolism were identified as the key biological processes and metabolic pathways for improving peanut salt tolerance. The hub genes include genes encoding ion transport (such as HAK8, CNGCs, NHX, NCL1) protein, aquaporin protein, CIPK11 (CBL-interacting serine/threonine-protein kinase 11), LEA5 (late embryogenesis abundant protein), POD3 (peroxidase 3), transcription factor, and MAPKKK3. There were some new salt-tolerant genes identified in peanut, including cytochrome P450, vinorine synthase, sugar transport protein 13, NPF 4.5, IAA14, zinc finger CCCH domain-containing protein 62, beta-amylase, fatty acyl-CoA reductase 3, MLO-like protein 6, G-type lectin S-receptor-like serine/threonine-protein kinase, and kinesin-like protein KIN-7B. The identification of key modules, biological pathways, and hub genes in this study enhances our understanding of the molecular mechanisms underlying salt tolerance in peanuts. This knowledge lays a theoretical foundation for improving and innovating salt-tolerant peanut germplasm.