FHY3 and FAR1 serve as positive regulators of the phyA-mediated far-red light signal pathway, influencing plant growth and development by regulating the expression of downstream genes. However, little is known about the FAR1/FHY3 family in Brassica species. A total of 21 members of the BnFAR1/FHY3 gene family were identified in the Brassica napus genome, exhibiting an uneven distribution across ten B. napus chromosomes. A phylogenetic analysis showed that the BnFAR1/FHY3 family could be divided into four subfamilies. Putative cis-elements in the BnFAR1/FHY3 promoter regions were also identified, which were potentially involved in phytohormone, light and abiotic stress responses (shading, low-temperature, etc.). Additionally, qRT-PCR results indicated that the expression levels of BnFAR1-10, BnFAR1-11, BnFAR1-21 and BnFAR1-4 decreased under shading stress. The expression of BnFAR1-10, BnFAR1-11 and BnFAR1-21 increased under low-temperature stress, whereas the expression of BnFAR1-4 did not change. In addition, the results of the tissue expression analysis showed that most of the genes exhibited the lowest expression in pollen and the highest expression in the 54-day silique. This study screened a batch of BnFHY3/BnFAR1 gene resources, which will contribute to further research on the functional characteristics of BnFHY3/BnFAR1 family members in growth, development and the stress response.