Salt stress seriously reduced the yield and quality of watermelon and restricted the sustainable development of the watermelon industry. However, the molecular mechanism of watermelon in response to salt stress is still unclear. In this study, 150 mmol·L−1 NaCl was used to deal with the seedlings of salt-tolerant and salt-sensitive watermelon varieties. Physiological characteristics showed that salt stress significantly reduced the biomass of watermelon seedlings and the accumulation of K+ in roots and leaves and significantly increased the content of Na+, Cl−, and malondialdehyde (MDA). Compared with the salt-sensitive variety, the salt-tolerant variety had higher K+ accumulation, lower Cl−, Cl− accumulation, and MDA content in roots and leaves. Then, RNA-seq was performed on roots and leaves in normal culture and under 150 mmol·L−1 NaCl treatment. A total of 21,069 genes were identified by RNA-seq analysis, of which 1412 were genes encoding transcription factors (TFs). In the comparison groups of roots and leaves, 122 and 123 shared differentially expressed genes (DEGs) were obtained, respectively. Gene ontology (GO) annotation and KEGG enrichment results showed that there were many identical GO terms and KEGG pathways in roots and leaves, especially the pathways that related to sugar or energy (ATP or NADP+/NADPH). In addition, some DEGs related to salt tolerance were identified, such as plant hormone indole-3-acetic acid (IAA) and gibberellin (GA) signal transduction pathway-related genes, K+/Na+/Ca2+-related genes, lignin biosynthesis-related genes, etc. At the same time, we also identified some TFs related to salt tolerance, such as AP2-EREBP, bZIP, bHLH, MYB, NAC, OFP, TCP, and WRKY and found that these TFs had high correlation coefficients with salt tolerance-related genes, indicating that they might have a potential regulatory relationship. Interestingly, one TCP TF (Cla97C09G174040) co-exists both in roots and leaves, and it is speculated that it may be regulated by miR319 to improve the salt tolerance of watermelon.