The formation and development of potato tissues and organs is a complex process regulated by a variety of genes and environmental factors. However, the regulatory mechanisms underlying the growth and development are still unclear. In this study, we used autotetraploid potato JC14 as experimental subject to analyze the transcriptome of root, stem and leaf at seedling, tuber formation and tuber expansion stages to explore the spatio-temporal expression pattern of genes and genetic development characteristics. The results identified thousands of differentially expressed genes and KEGG pathway enrichment analysis showed that these genes were mainly involved in defense response and carbohydrate metabolism pathways. A total of 12 co-expressed Gene modules were identified by Weighted Gene Co-expression Network Analysis (WGCNA), and 4 modules were screened out with the highest correlation with potato stem developmental traits. Core genes in the network were further investigated and functionally annotated by computing the connectivity of genes within the module. The results unveiled number of hub genes in stems at different developmental stages, including carbohydrate metabolism related genes, the defense response related genes, and transcription factors. These findings provide important leads for further understanding of the molecular regulation and genetic mechanisms of potato tissue development.