Xiaoyan 60 (XY60) is a new wheat variety bred in the laboratory of Zhensheng Li. After salt treatment, seedlings of XY60 maintain green leaves and produce longer roots than the high yielding cultivar Zhongmai 175 (ZM175). To explain these different phenotypes we carried out an RNA-Seq analysis using 12 samples from three tissues of both varieties subjected to salt and control treatments. By comparing data from the salt treated plants with the control, 703, 979, and 1197 differentially expressed genes (DEGs) were detected in new leaves, old leaves, and roots of XY60, respectively. The corresponding numbers for ZM175 were 613, 1401, and 1301. The most significantly enriched Gene Ontology (GO) terms and KEGG pathways were associated with polyunsaturated fatty acid (PUFA) metabolism in both new and old leaves from XY60. They were associated with photosynthesis and energy metabolism in ZM175. The most significantly enriched KEGG pathway in roots of both varieties was “glucosinolate biosynthesis”. In addition, jasmonic acid (JA) concentration in XY60 was higher than in ZM175, although it increased significantly in both varieties following salt treatment. Trends in relative expression levels of AOS, MYC2, and JAZ revealed by qRT-PCR were concordant with those from RNA-Seq. Our results suggest that PUFAs may contribute to salt tolerance in common wheat by enhancing the photosynthetic system and JA-related pathways.