Wild soybean, the progenitor and close relative of cultivated soybean, has an excellent environmental adaptation ability and abundant resistance genes. Expansins, as a class of cell wall relaxation proteins, have important functions in regulating plant growth and stress resistance. In the present study, we identified a total of 75 members of the expansin family on the basis of recent genomic data published for wild soybean. The predicted results of promoter elements structure showed that wild soybean expansin may be associated with plant hormones, stress responses, and growth. Basal transcriptome data of vegetative organs suggest that the transcription of expansin members has some organ specificity. Meanwhile, the transcripts of some members had strong responses to salt, low temperature and drought stress. We screened and obtained an expansin gene, GsEXPB1, which is transcribed specifically in roots and actively responds to salt stress. The results of A. tumefaciens transient transfection showed that this protein was localized in the cell wall of onion epidermal cells. We initially analyzed the function of GsEXPB1 by a soybean hairy root transformation assay and found that overexpression of GsEXPB1 significantly increased the number of hairy roots, root length, root weight, and the tolerance to salt stress. This research provides a foundation for subsequent studies of expansins in wild soybean.