Fatty acids are essential body nutrients. Although the content of oil in common buckwheat grain is not high, it contains high polyunsaturated fatty acids, and the content of unsaturated fatty acids is about 40%. Fatty acid desaturase(FAD) is a key enzyme for the formation of unsaturated fatty acids. The study of FAD genes in common buckwheat is important for understanding the formation and regulation of polyunsaturated fatty acids. In this study,a total of 10 full-length FAD genes were identified by Blastp from the common buckwheat genomic database by using the Arabidopsis membrane-bound fatty acid desaturase(FAD) genes as queries. The genetic characteristics, evolution, conserved domains, secondary and tertiary structure of proteins in common buckwheat FAD were analyzed.The results showed that 10 FeFAD genes were divided into 6 sub-groups. The analysis of gene characteristics showed that the open reading frame of FeFAD genes was among 900～1 374 bp, and the isoelectric point was among 6.83～9.23. All FeFAD genes contain introns, and FeFAD6 contains the largest number of introns, which number is 10. FeFAD4 contains TMEM189_Bdmain conserved domain, whereas most FeFADs contain conserved fatty acid desaturase domains. FeSLDs contains not only fatty acid desaturase but also Cyt-b5 domain. Most FeFADs contain three conserved histidine sequences of HXXXH, HXXHH and HXXHH, except FeFAD4, which contains two conserved histidine sequences of HXXXH and HXXHH. The number of secondary amino acids predicted that FeFADs were mainly α-helix and random coil. The prediction of tertiary structure shows that most of the tertiary structures of FeFADs have their own unique structures. The results of this study will provide a theoretical basis for exploring the function of fatty acid desaturase gene in common buckwheat.