Glycine-rich RNA-binding proteins (GR-RBPs) are involved in cold shock response of plants as RNA chaperones facilitating mRNA transport, splicing and translation. GR-RBPs are bipartite proteins containing a RNA recognition motif (RRM) followed by a glycine-rich region. Here, we studied the structural basis of nucleic acid binding of full-length Nicotiana tabacum GR-RBP1. NMR studies of NtGR-RBP1 show that the glycine-rich domain, while intrinsically disordered, is responsible for mediating self-association by transient interactions with its RRM domain (NtRRM). Both NtGR-RBP1 and NtRRM bind specifically and with low micromolar affinity to RNA and single-stranded DNA. The solution structure of NtRRM shows that it is a canonical RRM domain. A HADDOCK model of the NtRRM–RNA complex, based on NMR chemical shift and NOE data, shows that nucleic acid binding results from a combination of stacking and electrostatic interactions with conserved RRM residues. Finally, DNA melting experiments demonstrate that NtGR-RBP1 is more efficient in melting CTG containing nucleic acids than isolated NtRRM. Together, our study supports the model that self-association of GR-RBPs by the glycine-rich region results in cooperative unfolding of non-native substrate structures, thereby enhancing its chaperone function.