Potato (Solanum tuberosum L.) is an important staple food worldwide. However, its growth has been heavily suppressed by salt stress. The molecular mechanisms of salt tolerance in potato remain unclear. It has been shown that the tetraploid potato Longshu No. 5 is a salt-tolerant genotype. Therefore, in this study we conducted research to identify salt stress response genes in Longshu No. 5 using a NaCl treatment and time-course RNA sequencing. The total number of differentially expressed genes (DEGs) in response to salt stress was 5508. Based on Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis, it was found that DEGs were significantly enriched in the categories of nucleic acid binding, transporter activity, ion or molecule transport, ion binding, kinase activity and oxidative phosphorylation. Particularly, the significant differential expression of encoding ion transport signaling genes suggests that this signaling pathway plays a vital role in salt stress response in potato. Finally, the DEGs in the salt response pathway were verified by Quantitative real-time PCR (qRT-PCR). These results provide valuable information on the salt tolerance of molecular mechanisms in potatoes, and establish a basis for breeding salt-tolerant cultivars.