The domain of unknown function 668 (DUF668) is a gene family that plays a vital role in responses to adversity coercion stresses in plant. However, the function of the DUF668 gene family is not fully understood in sweet potato. In this study, bioinformatics methods were used to analyze the number, physicochemical properties, evolution, structure, and promoter cis-acting elements of the IbDUF668 family genes, and RNA-seq and qRT-PCR were performed to detect gene expression and their regulation under hormonal and abiotic stress. A total of 14 IbDUF668 proteins were identified in sweet potato, distributed on nine chromosomes. By phylogenetic analysis, IbDUF668 proteins can be divided into two subfamilies. Transcriptome expression profiling revealed that many genes from DUF668 in sweet potato showed specificity and differential expression under cold, heat, drought, salt and hormones (ABA, GA3 and IAA). Four genes (IbDUF668-6, 7, 11 and 13) of sweet potato were significantly upregulated by qRT-PCR under ABA, drought and NaCl stress. Results suggest that the DUF668 gene family is involved in drought and salt tolerance in sweet potato, and it will further provide the basic information of DUF668 gene mechanisms in plants.