Stress-associated proteins (SAP) that contain the A20/AN1 zinc-finger domain play important roles in plants abiotic stress responses. However, little is known about the SAP gene family in Brassica napus (genome AnAnCnCn), was formed by recent allopolyploidy between ancestors of Brassica rapa (genome ArAr) and Brassica oleracea (genome CoCo). To explore the distribution and expression patterns of these genes, a genome-wide identification and a systematic analysis of genes in the SAP family in B. napus were performed. A total of 57 genes encoding SAP were identified, and subsequently classified into 5 groups. In contrast to results seen in other plant species, further analyses of gene structures and conserved protein motifs revealed that a large percentage of the BnaSAP (16/57) genes were A20-type or AN1-type SAP genes, most of which were not found to have homologous genes in B. rapa or B. oleracea. The cis-elements of the BnaSAP promoters, and BnaSAP gene expression levels in different tissues, and under different stress treatments, were also investigated based on RNA-seq data. All the typical A20-AN1-type and AN1-AN1(-C2H2)-type BnaSAP genes were constitutively expressed among all tissues, except 4 members in Group II. In contrast, almost all A20 type and AN1 type members showed very low detection levels in all the tested rapeseed tissues from which the transcriptome data was derived. Additionally, most of the typical A20-AN1-type and AN1-AN1-type BnaSAP genes were found to be induced by multiple stresses and phytohormones. Among the identified BnaSAP genes, four members of Group III (BnaA07g15770D, BnaC06g14100D, BnaC04g27800D, and BnaC08g24010D) were induced following various low-temperature stresses in leaves, and were induced by NaCl and PEG stress in roots. BnaA06g02460D and BnaC06g04440D from Group IV were induced by heat stress, while BnaA06g31640D and BnaC07g25010D from Group V were induced by heat stress and salicylic acid (SA) treatment. This study provides a comprehensive analysis of SAP genes in rapeseed, and may aid in future efforts to identify the functions of A20/AN1-type proteins and the responses of rapeseed under a variety of abiotic stresses.