Sweet potato is an important food and bio-energy crop, and investigating the mechanisms underlying salt tolerance will provide information for salt-tolerant breeding of this crop. Here, the root transcriptomes of the salt-sensitive variety Lizixiang and the salt-tolerant line ND98 were compared to identify the genes and pathways involved in salt stress responses. In total, 8,744 and 10,413 differentially expressed genes (DEGs) in Lizixiang and ND98, respectively, were involved in salt responses. A lower DNA methylation level was detected in ND98 than in Lizixiang. In both genotypes, the DEGs, which function in phytohormone synthesis and signalling and ion homeostasis, may underlie the different degrees of salt tolerance. Significant up-regulations of the genes involved in the jasmonic acid (JA) biosynthesis and signalling pathways and ion transport, more accumulation of JA, a higher degree of stomatal closure and a lower level of Na+ were found in ND98 compared to Lizixiang. This is the first report on transcriptome responses to salt tolerance in sweet potato. These results reveal that the JA signalling pathway plays important roles in the response of sweet potato to salt stress. This study provides insights into the mechanisms and genes involved in the salt tolerance of sweet potato.