The RNA-binding glycine-rich proteins (RBGs) of the glycine-rich protein family play vital roles in regulating gene expression both at the transcriptional and post-transcriptional levels. However, the members and functions in response to abiotic stresses of the RBG gene family remain unclear in Brassica oleracea. In this study, a total of 19 BoiRBG genes were identified through genome-wide analysis in broccoli. The characteristics of BoiRBG sequences and their evolution were examined. An analysis of synteny indicated that the expansion of the BoiRBG gene family was primarily driven by whole-genome duplication and tandem duplication events. The BoiRBG expression patterns revealed that these genes are involved in reaction to diverse abiotic stress conditions (i.e., simulated drought, salinity, heat, cold, and abscisic acid) and different organs. In the present research, the up-regulation of BoiRBGA13 expression was observed when subjected to both NaCl-induced and cold stress conditions in broccoli. Moreover, the overexpression of BoiRBGA13 resulted in a noteworthy reduction in taproot lengths under NaCl stress, as well as the inhibition of seed germination under cold stress in broccoli, indicating that RBGs play different roles under various stresses. This study provides insights into the evolution and functions of BoiRBG genes in Brassica oleracea and other Brassicaceae family plants.