The R2R3-MYB sub-family proteins are composed of most members of MYB (v-Myb avian myeloblastosis viral oncogene homolog) protein, a plant-specific transcription factor (TF) that is classified into four classes depending on the number of MYB repeats. R2R3-MYB TFs are involved in physiological and biochemical processes. However, the functions of the Brassica napus R2R3-MYB genes are still mainly unknown. In this study, 35 Brassica napus MYB (BnaMYB) genes were screened in the genome of Brassica napus, and details about their physical and chemical characteristics, evolutionary relationships, chromosome locations, gene structures, three-dimensional protein structures, cis-acting promoter elements, and gene duplications were uncovered. The BnaMYB genes have undergone segmental duplications and positive selection pressure, according to evolutionary studies. The same subfamilies have similar intron–exon patterns and motifs, according to the genes’ structure and conserved motifs. Additionally, through cis-element analysis, many drought-responsive and other stress-responsive cis-elements have been found in the promoter regions of the BnaMYB genes. The expression of the BnaMYB gene displays a variety of tissue-specific patterns. Ten lignin-related genes were chosen for drought treatment. Our research screened four genes that showed significant upregulation under drought stress, and thus may be important drought-responsive genes. The findings lay a new foundation for understanding the complex mechanisms of BnaMYB in multiple developmental stages and pathways related to drought stress in rapeseed.