Although the functional roles of glycine-rich RNA-binding proteins (GRPs) during stress adaptation have been extensively evaluated in Arabidopsis thaliana and rice (Oryza sativa), the stress-responsive roles of a majority of GRPs have not been characterized in other plant species including rapeseed (Brassica napus). Here, the characteristic features and stress-responsive expression patterns of GRPs in B. napus (BnGRPs) were investigated. The genome of B. napus contains seven closely related BnGRPs, where the amino acid sequences of a well-conserved RNA-recognition motif at the N-terminal region are highly similar to each other but the sequences of the C-terminal glycine-rich region vary greatly among different BnGRPs. The transcript levels of all BnGRPs were markedly upregulated by cold stress, while their expression was significantly downregulated by dehydration or high salinity stress. Among the seven BnGRPs evaluated, BnGRP1 was characterized in more detail for its cellular localization and functional role as an RNA chaperone under cold stress. Cold-induced BnGRP1 successfully complemented the cold-sensitive phenotype of Escherichia coli mutant BX04 cells under cold stress, and harbored DNA- and RNA-melting abilities. Ectopic expression of BnGRP1 in Arabidopsis resulted in accelerated seed germination and enhanced freezing tolerance of the plant under cold or freezing stress. Collectively, the results of this study support the emerging idea that GRPs are functionally conserved RNA chaperones during the cold adaptation process in diverse plant species.