B-box (BBX) proteins are one kind of zinc-finger transcription factors that play critical roles in plant development, growth and multiple stress responses. Ipomoea trifida is the closest diploid wild ancestor of sweet potato, and its genome has been released. However, no comprehensive study has yet been carried out on the BBX genes in Ipomoea species. In this study, a total of 34 BBX (ItfBBX) genes were identified in Ipomoea trifida, and were phylogenetically divided into five clades. BBX members within the same clade showed similar domain organizations, suggesting similarity of biological function potentially. Evolutionary analysis indicated that segmental duplications played a major role in the ItfBBX gene expansion, and gene loss has frequently occurred after Ipomoea whole-genome triplication event. On the basis of the transcriptome data, we identified ItfBBX genes with tissue specific and dynamic stress response expression patterns. With the quantitative real-time PCR analysis, we discovered highly divergent stress-response patterns of ItfBBX genes (such as ItfBBX7, ItfBBX8, ItfBBX12, ItfBBX14 and ItfBBX22) in root and leaf, implying their functional conservation and divergence. Furthermore, the transient expression assay demonstrated that eight selected ItfBBXs were localized in nucleus. Our study provides the first step in systemic analyses of the ItfBBX genes, and will be useful to understand the functional characterization of BBX genes in Ipomoea species.