The formation and development of potato tissues and organs is a complex process regulated by a variety of genes and environmental factors. The regulatory mechanisms underlying the growth and development are still unclear. In this work, we aimed to explore the changes in gene expression patterns and genetic characteristics of potato tissues throughout different developmental stages. To achieve this, we used autotetraploid potato JC14 as an experimental subject to analyze the transcriptome of the root, stem, and leaf at the seedling, tuber formation, and tuber expansion stages. The results revealed thousands of differentially expressed genes, predominantly involved in defense response and carbohydrate metabolism according to KEGG pathway enrichment analysis. Weighted gene co-expression network analysis (WGCNA) revealed a total of 12 co-expressed gene modules, with 4 modules showing the highest correlation with potato stem development. By calculating the connectivity of genes within the module, hub genes were identified, and functional annotations were subsequently performed. A total of 40 hub genes from the four modules were identified, and their functions were found to be related to carbohydrate metabolism, defense response, and transcription factors. These findings provide important insights for further understanding of the molecular regulation and genetic mechanisms involved in potato tissue development.